Loop-and-allied QG bibliography

[marcus]

http://arxiv.org/abs/0910.4028
Metric Lagrangians with two propagating degrees of freedom
Kirill Krasnov
4 pages
(Submitted on 21 Oct 2009)
"There exists a large class of generally covariant metric Lagrangians that contain only local terms and describe two propagating degrees of freedom. Trivial examples can be be obtained by applying a local field redefinition to the Lagrangian of general relativity, but we show that the class of two propagating degrees of freedom Lagrangians is much larger. Thus, we exhibit a large family of non-local field redefinitions that map the Einstein-Hilbert Lagrangian into ones containing only local terms. These redefinitions have origin in the topological shift symmetry of BF theory, to which GR is related in Plebanski formulation, and can be computed order by order as expansions in powers of the Riemann curvature. At its lowest non-trivial order such a field redefinition produces the (Riemann)^3 invariant that arises as the two-loop quantum gravity counterterm. Possible implications for quantum gravity are discussed."

 

[John86]

http://arxiv.org/abs/0910.4289
Aspects of nonrelativistic quantum gravity
Authors: Johan Hansson
(Submitted on 22 Oct 2009)
Abstract: A nonrelativistic approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach can be used to point out problems and prospects inherent in a more exact theory of quantum gravity, yet to be discovered. Nonrelativistic quantum gravity, e.g., shows promise for prohibiting black holes altogether (which would eliminate singularities and also solve the black hole information paradox), gives gravitational radiation even in the spherically symmetric case, and supports non-locality (quantum entanglement). Its predictions should also be testable at length scales well above the "Planck scale", by high-precision experiments feasible with existing technology.

http://arxiv.org/abs/0910.4017
Wormhole Spaces: the Common Cause for the Black Hole Entropy-Area Law,the Holographic Principle and Quantum Entanglement
Authors: Manfred Requardt
(Submitted on 21 Oct 2009)
Abstract: We present strong arguments that the deep structure of the quantum vacuum contains a web of microscopic wormholes or short-cuts. We develop the concept of wormhole spaces and show that this web of wormholes generate a peculiar array of long-range correlations in the patterns of vacuum fluctuations on the Planck scale. We conclude that this translocal structure represents the common cause for both the BH-entropy-area law, the more general holographic principle and the entanglement phenomena in quantum theory. In so far our approach exhibits a common structure which underlies both gravity and quantum theory on a microscopic scale. A central place in our analysis is occupied by a quantitative derivation of the distribution laws of microscopic wormholes in the quantum vacuum. This makes it possible to address a number of open questions and controversial topics in the field of quantum gravity.

http://arxiv.org/abs/0910.2600
Reformulating the Schrodinger equation as a Shabat-Zakharov system
Authors: Petarpa Boonserm (Chulalongkorn University), Matt Visser (Victoria University of Wellington)
(Submitted on 14 Oct 2009)
Abstract: We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear

 

[marcus]

http://arxiv.org/abs/0910.4951
Asymptotic safety in gravity and sigma models
R. Percacci
Talk given at International Workshop on Continuum and Lattice Approaches to Quantum Gravity, Brighton, United Kingdom, 17-19 Sep 08. To appear in PoS
(Submitted on 26 Oct 2009)
"There are deep analogies between Einstein's theory of gravity and the nonlinear sigma models. It is suggested that these similarities may extend also to the ultraviolet behaviour, in the sense that both theories could turn out to be asymptotically safe."

http://arxiv.org/abs/0910.4837
Asymmetric cyclic evolution in polymerised cosmology
Orest Hrycyna, Jakub Mielczarek, Marek Szydlowski
10 pages, 4 figs
(Submitted on 26 Oct 2009)
"The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase space. We have shown that the cyclic solutions are generic. The exact solution for polymerised cosmology is also obtained. Two basic cases are investigated, the polymerised scalar field and the polymerised gravitational and scalar field part. In the former the division on the cyclic and non-cyclic behaviour is established following the sign of the cosmological constant. The value of the cosmological constant is upper bounded purely from the dynamical setting."

 

[MTd2]

http://arxiv.org/abs/0910.4938

Running Gauge Coupling in Asymptotically Safe Quantum Gravity

Jan-Eric Daum, Ulrich Harst, Martin Reuter
(Submitted on 26 Oct 2009)
We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.

 

[marcus]

http://arxiv.org/abs/0910.5167
Gravity from a Particle Physicists' perspective
R. Percacci
Lectures given at the Fifth International School on Field Theory and Gravitation, Cuiaba, Brazil April 20-24 2009. To appear in PoS
(Submitted on 27 Oct 2009)
"In these lectures I review the status of gravity from the point of view of the gauge principle and renormalization, the main tools in the toolbox of theoretical particle physics. In the first lecture I start from the old question "in what sense is gravity a gauge theory?" I will reformulate the theory of gravity in a general kinematical setting which highlights the presence of two Goldstone boson-like fields, and the occurrence of a gravitational Higgs phenomenon. The fact that in General Relativity the connection is a derived quantity appears to be a low energy consequence of this Higgs phenomenon. From here it is simple to see how to embed the group of local frame transformations and a Yang Mills group into a larger unifying group, and how the distinction between these groups, and the corresponding interactions, derives from the VEV of an order parameter. I will describe in some detail the fermionic sector of a realistic "GraviGUT" with SO(3,1)xSO(10) \subset SO(3,11). In the second lecture I will discuss the possibility that the renormalization group flow of gravity has a fixed point with a finite number of attractive directions. This would make the theory well behaved in the ultraviolet, and predictive, in spite of being perturbatively nonrenormalizable. There is by now a significant amount of evidence that this may be the case. There are thus reasons to believe that quantum field theory may eventually prove sufficient to explain the mysteries of gravity."

[my note: PoS is Proceedings of Science, an online resource maintained by SISSA, the Italian Institute for Advanced Studies at Trieste]

 

[MTd2]

http://arxiv.org/abs/0910.5401

The Effective Potential of the Conformal Factor in Asymptotically Safe Quantum Gravity

Jan-Eric Daum, Martin Reuter
(Submitted on 28 Oct 2009)
The effective potential of the conformal factor in the effective average action approach to Quantum Einstein Gravity is discussed. It is shown, without invoking any truncation or other approximations, that if the theory has has a non-Gaussian ultraviolet fixed point and is asymptotically safe the potential has a characteristic behavior near the origin. This behavior might be observable in numerical simulations.

 

[John86]

http://arxiv.org/abs/0910.5377
Bose-Einstein condensed supermassive black holes: a case of renormalized quantum field theory in curved space-time
Authors: Theo M. Nieuwenhuizen, Vaclav Spicka
(Submitted on 28 Oct 2009)
Abstract: This paper investigates the question whether a realistic black hole can be in principal similar to a star, having a large but finite redshift at its horizon. If matter spreads throughout the interior of a supermassive black hole with mass $M\sim10^9M_\odot$, it has an average density comparable to air and it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field describing H atoms is coupled to the curvature scalar with dimensionless coupling $\xi$. In the Bose-Einstein condensed groundstate an exact, self-consistent solution for the metric occurs for a certain large value of $\xi$, quadratic in the black hole mass. It is put forward that $\xi$ is set by proper choice of the background metric as a first step of a renormalization approach, while otherwise the non-linearities are small. The black hole has a hair, the binding energy. Fluctuations about the ground state are considered.

 

[atyy]

http://physics.aps.org/articles/v2/90
Tensor networks—a new tool for old problems
Subir Sachdev
A new renormalization group approach that maps lattice problems to tensor networks may hold the key to solving seemingly intractable models of strongly correlated systems in any dimension.

Wen's talk is also helpful http://dao.mit.edu/~wen/talks/09Dresden.pdf

 

[marcus]

http://arxiv.org/abs/0910.5836
Can the Arrow of Time be understood from Quantum Cosmology?
Claus Kiefer
(Submitted on 30 Oct 2009)
I address the question whether the origin of the observed arrow of time can be derived from quantum cosmology. After a general discussion of entropy in cosmology and some numerical estimates, I give a brief introduction into quantum geometrodynamics and argue that this may provide a sufficient framework for studying this question. I then show that a natural boundary condition of low initial entropy can be imposed on the universal wave function. The arrow of time is then correlated with the size of the Universe and emerges from an increasing amount of decoherence due to entanglement with unobserved degrees of freedom. Remarks are also made concerning the arrow of time in multiverse pictures and scenarios motivated by dark energy.
Comments: 14 pages, to appear in "The Arrow of Time", ed. by L. Mersini-Houghton and R. Vaas

Brief mention--possible tangential relevance to 4D QG:
http://arxiv.org/abs/0910.5891
Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks
Samuel J. Lomonaco, Louis H. Kauffman

http://arxiv.org/pdf/0910.5733
Decoherence in an Interacting Quantum Field Theory: The Vacuum Case
Jurjen F. Koksma (Utrecht), Tomislav Prokopec (Utrecht), Michael G. Schmidt (Heidelberg)

 

[MTd2]

"Quantum Knots and Lattices, or a Blueprint for Quantum Systems that Do Rope Tricks" is broken. The pictures of the paper are messed up. Is is not available at the time of this post. Look for v2, when it shows up.

 

[marcus]

http://arxiv.org/abs/0911.0386
Renormalization Group Flow in Scalar-Tensor Theories. I
Gaurav Narain, Roberto Percacci
18 pages, 10 figures
(Submitted on 2 Nov 2009)
"We study the renormalization group flow in a class of scalar-tensor theories involving at most two derivatives of the fields. We show in general that minimal coupling is self consistent, in the sense that when the scalar self couplings are switched off, their beta functions also vanish. Complete, explicit beta functions that could be applied to a variety of cosmological models are given in a five parameter truncation of the theory in d=4. In any dimension d>2 we find that the flow has only a 'Gaussian Matter' fixed point, where all scalar self interactions vanish but Newton's constant and the cosmological constant are nontrivial. The properties of these fixed points can be studied algebraically to some extent. In d=3 we also find a gravitationally dressed version of the Wilson-Fisher fixed point, but it seems to have unphysical properties. These findings are in accordance with the hypothesis that these theories are asymptotically safe."

http://arxiv.org/abs/0911.0394
Renormalization Group Flow in Scalar-Tensor Theories. II
Gaurav Narain, Christoph Rahmede
14 pages
(Submitted on 2 Nov 2009)
"We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in d=4 for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in d=4 including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional."

http://arxiv.org/abs/0911.0401
Spectral geometry as a probe of quantum spacetime
Dario Benedetti, Joe Henson
25 pages, 6 figures
(Submitted on 2 Nov 2009)
"Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity -- the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifgarbagez gravity, among other approaches to quantum gravity."

 

[marcus]

http://arxiv.org/abs/0911.0437
Fractal Space-Time from Spin-Foams
Elena Magliaro, Claudio Perini, Leonardo Modesto
5 pages, 2 figures
(Submitted on 2 Nov 2009)
"In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from ~ 2 to 4, across a ~1.5 phase, when the energy of a probe scalar field decreases from high E \lesssim E_P/25 to low energy. The spectral dimension at the Planck scale E \approx E_P depends on the areas spectrum used in the calculation. For three different spectra l_P^2 \sqrt{j(j+1)}, l_P^2 (2 j+1) and l_P^2 j we find respectively dimension ~ 2.31, 2.45 and 2.08."

http://arxiv.org/abs/0911.0543
The volume operator in covariant quantum gravity
You Ding, Carlo Rovelli
9 pages
(Submitted on 3 Nov 2009)
"A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space."

 

[MTd2]

http://arxiv.org/abs/0911.0437

The volume operator in covariant quantum gravity

You Ding, Carlo Rovelli
(Submitted on 3 Nov 2009)
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.

 

[John86]

http://arxiv.org/abs/0909.5421
In, Through and Beyond the Planck Scale
Authors: Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 29 Sep 2009 (v1), last revised 31 Oct 2009 (this version, v2))
Abstract: In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordstr\"om-like metric is self-dual in the sense of T-duality: the form of the metric is invariant under the exchange r -> a0/r where a0 is proportional to the minimum area in LQG. Of particular interest, the symmetry imposes that if an observer at infinity sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (near r=0) sees a dual mass proportional to m_P^2/m. We then show that small LQBHs are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately 10^(-5) m_P and emit radiation with a typical energy of about 10^(13) - 10^(14) eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.

http://arxiv.org/abs/0908.4224
Stochastic quantization and the role of time in quantum gravity
Authors: J. Ambjorn, R. Loll, W. Westra, S. Zohren
(Submitted on 28 Aug 2009 (v1), last revised 1 Nov 2009 (this version, v2))
Abstract: We show that the noncritical string field theory developed from two-dimensional quantum gravity in the framework of causal dynamical triangulations can be viewed as arising through a stochastic quantization. This requires that the proper time appearing in the string field theory be identified with the stochastic time of the stochastic formulation. The framework of stochastic quantization gives rise to a natural nonperturbative quantum Hamiltonian, which incorporates a sum over all spacetime topologies. We point out that the external character of stochastic time is a feature that pertains more generally to the proper time or distance appearing in nonperturbative correlation functions in quantum gravity.

http://arxiv.org/abs/0910.5733
Decoherence in an Interacting Quantum Field Theory: The Vacuum Case
Authors: Jurjen F. Koksma (Utrecht University), Tomislav Prokopec (Utrecht University), Michael G. Schmidt (Heidelberg University)
(Submitted on 29 Oct 2009)
Abstract: We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a "system field" and an "environment field" that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.

 

[MTd2]

http://arxiv.org/abs/0911.1020

Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms

Giovanni Amelino-Camelia, Claus Laemmerzahl, Flavio Mercati, Guglielmo M. Tino
(Submitted on 5 Nov 2009)
We use the results of ultra-precise cold-atom-recoil experiments to constrain the form of the energy-momentum dispersion relation, a structure that is expected to be modified in several quantum-gravity approaches. Our strategy of analysis applies to the nonrelativistic (small speeds) limit of the dispersion relation, and is therefore complementary to an analogous ongoing effort of investigation of the dispersion relation in the ultrarelativistic regime using observations in astrophysics. For the leading correction in the nonrelativistic limit the exceptional sensitivity of cold-atom-recoil experiments remarkably allows us to set a limit within a single order of magnitude of the desired Planck-scale level, thereby providing the first example of Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments. For the next-to-leading term we obtain a limit which is a few orders of magnitude away from the Planck scale, but still amounts to the best limit on a class of Lorentz-symmetry test theories that has been extensively used to investigate the hypothesis of "deformation" (rather than breakdown) of spacetime symmetries.

 

[John86]

http://arxiv.org/abs/0911.1063
The cosmological constant and higher dimensional dilatation symmetry
Authors: C. Wetterich
(Submitted on 5 Nov 2009)
Abstract: We discuss the hypothesis of a fixed point for quantum gravity coupled to a scalar, in the limit where the scalar field goes to infinity, accompanied by a suitable scaling of the metric. We propose that no scalar potential is present for the dilatation symmetric quantum effective action at the fixed point. Dimensional reduction of such a higher dimensional effective action leads to solutions with a vanishing effective four-dimensional constant. Under rather general circumstances these are the only quasistatic stable solutions with finite four-dimensional gravitational constant. If cosmological runaway solutions approach the fixed point as time goes to infinity, the cosmological constant vanishes asymptotically. For our old Universe the fixed point is not yet reached completely, resulting in a tiny amount of dark energy, comparable to dark matter. We discuss explicitly higher dimensional geometries which realize such asymptotic solutions for $t\to\infty$. They include Ricci-flat spaces as well as warped spaces, potentially with singularities.

 

[MTd2]

http://arxiv.org/abs/0911.1132

Polynomial 6j-Symbols and States Sums

Nathan Geer, Bertrand Patureau-Mirand
(Submitted on 6 Nov 2009)
For q a root of unity of order 2r, we give explicit formulas of a family of 3-variable Laurent polynomials J_{i,j,k} with coefficients in Z[q] that encode the 6j-symbols associated with nilpotent representations of U_qsl_2. For a given abelian group G, we use them to produce a state sum invariant tau^r(M,L,h_1,h_2) of a quadruplet (compact 3-manifold M, link L inside M, homology class h_1\in H_1(M,Z), homology class h_2\in H_2(M,G)) with values in a ring R related to G. The formulas are established by a ``skein'' calculus as an application of the theory of modified dimensions introduced in [arXiv:0711.4229]. For an oriented 3-manifold M, the invariants are related to TV(M,L,f\in H^1(M,C^*)) defined in [arXiv:0910.1624] from the category of nilpotent representations of U_qsl_2. They refine them as TV(M,L,f)= Sum_h tau^r(M,L,h,f') where f' correspond to f with the isomorphism H_2(M,C^*) ~ H^1(M,C^*).

http://arxiv.org/abs/0911.1132

String-nets, single and double-stranded quantum loop gases for non-Abelian anyons

Andrea Velenich, Claudio Chamon, Xiao-Gang Wen
(Submitted on 5 Nov 2009)
String-net condensation can give rise to non-Abelian anyons whereas loop condensation usually gives rise to Abelian anyons. It has been proposed that generalized quantum loop gases with non-orthogonal inner products can produce non-Abelian anyons. We detail an exact mapping between the string-net and the generalized loop models and explain how the non-orthogonal products arise. We also introduce a loop model of double-stranded nets where quantum loops with an orthogonal inner product and local interactions supports non-Abelian Fibonacci anyons. Finally we emphasize the origin of the sign problem in such systems and its consequences on the complexity of their ground state wave functions.

 

[marcus]

http://arxiv.org/abs/0911.1719
Bosonic Colored Group Field Theory
Joseph Ben Geloun, Jacques Magnen, Vincent Rivasseau
ICMPA-MPA/2009/24, LPT-2009-93
(Submitted on 9 Nov 2009)
"Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman amplitudes in the 'ultraspin' (large spin) limit. The results are generalized in any dimension. Finally integrating out two colors we write a new representation which could be useful for the constructive analysis of this type of models."

http://arxiv.org/abs/0911.1625
Loop Quantum Cosmology corrections on gravity waves produced during primordial inflation
J. Grain
To be published in the AIP Proceedings of the 'Invisible Universe International Conference', UNESCO-Paris, June 29-July 3, 2009; 9 pp., 4 Figs
(Submitted on 9 Nov 2009)
"Loop Quantum Gravity (L.Q.G.) is one of the two most promising tentative theory for a quantum description of gravity. When applied to the entire universe, the so-called Loop Quantum Cosmology (L.Q.C.) framework offers microscopical models of the very early stages of the cosmological history, potentially solving the initial singularity problem via bouncing solutions or setting the universe in the appropriate initial conditions for inflation to start, via a phase of super-inflation. More interestingly, L.Q.C. could leave a footprint on cosmological observables such as the Cosmic Microwave Background (CMB) anisotropies. Focusing on the modified dispersion relation when holonomy and inverse-volume corrections arising from the L.Q.C. framework are considered, it is shown that primordial gravity waves generated during inflation are affected by quantum corrections. Depending on the type of corrections, the primordial tensor power spectrum is either suppressed or boosted at large length scales, and strongly departs from the power-law behavior expected in the standard scenario."

http://arxiv.org/abs/0911.1403
A Physical Interpretation of Gravitational Field Equations
T. Padmanabhan
Based on the Plenary talk given at the International Conference on `Invisible Universe', 29 June- 3 July, 2009 Paris; to appear in the Proceedings; 2 figures; 16 pages
(Submitted on 7 Nov 2009)
"It is possible to provide a thermodynamic interpretation for the field equations in any diffeomorphism invariant theory of gravity. This insight, in turn, leads us to the possibility of deriving the gravitational field equations from another variational principle without using the metric as a dynamical variable. I review this approach and discuss its implications."

http://arxiv.org/abs/0911.1700
Four-Dimensional Spin Foam Perturbation Theory
Joao Faria Martins, Aleksandar Mikovic
23 pages, 6 figures
(Submitted on 9 Nov 2009)
"We formulate the four-dimensional spin-foam perturbation theory for a BF-theory with a B\wedge B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group U_q (\mathfrak{g}) where \mathfrak{g} is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners \L\otimes \L \to A, where A is the adjoint representation of \mathfrak{g}, is 1-dimensional for each irrep L. We calculate the partition function Z in the dilute-gas limit for special classes of triangulations, which we conjecture to exist exist on any 4-manifold M. We prove that the first order perturbative contribution vanishes, so that we define a dilute-gas limit by using the second order contribution. Furthermore, we relate Z to the partition function for the F\wedge F theory."

 

[John86]

http://arxiv.org/abs/0911.1479
Is the spacetime metric Euclidean rather than Lorentzian?
Authors: Rafael D. Sorkin (Perimeter Institute and Syracuse University)
(Submitted on 8 Nov 2009)
Abstract: My answer to the question in the title is "No". In support of this point of view, we analyze some examples of saddle-point methods, especially as applied to quantum "tunneling" in nonrelativistic particle mechanics and in cosmology. Along the way we explore some of the interrelationships among different ways of thinking about path-integrals and saddle-point approximations to them

 

[marcus]

http://arxiv.org/abs/0911.1945
Topological Graph Polynomials in Colored Group Field Theory
Razvan Gurau
(Submitted on 10 Nov 2009)
"In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph \mathfrak{G}_{\partial} of an open graph \mathfrak{G} and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension."

 

[MTd2]

http://arxiv.org/abs/0911.2204

Recurrence relations for spin foam vertices

Valentin Bonzom, Etera R. Livine, Simone Speziale
(Submitted on 11 Nov 2009)
We study recurrence relations for various Wigner 3nj-symbols and the non-topological 10j-symbol. For the 6j-symbol and the 15j-symbols which correspond to basic amplitudes of 3d and 4d topological spin foam models, recurrence relations are obtained from the invariance under Pachner moves and can be interpreted as quantizations of the constraints of the underlying classical field theories. We also derive recurrences from the action of holonomy operators on spin network functionals, making a more precise link between the topological Pachner moves and the classical constraints. Interestingly, our recurrence relations apply to any SU(2) invariant symbol, depending on the cycles of the corresponding spin network graph. Another method is used for non-topological objects such as the 10j-symbol and pseudo-isoceles 6j-symbols. The recurrence relations are also interpreted in terms of elementary geometric properties. Finally, we discuss the extension of the recurrences to take into account boundary states which leads to equations similar to Ward identities for correlation functions in the Barrett-Crane model.

http://arxiv.org/abs/0911.2135

Approaches To Quantum Gravity

Cecilia Flori
(Submitted on 11 Nov 2009)
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed.
In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme, inheriting all the formalism of both GR and Quantum Theory, as it tries to bring to its logical extreme consequences the possibility of combining the two. On the other hand, the Topos approach involves the idea that a radical change of perspective is needed in order to solve the problem of quantum gravity, especially in regard to the fundamental concepts of `space' and `time'. Given the partial successes of both approaches, the hope is that it might be possible to find a common ground in which each approach can enrich the other.

 

[marcus]

http://arxiv.org/abs/0911.2404
Emergent Dirac Hamiltonians in Quantum Gravity
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
1 figure
(Submitted on 12 Nov 2009)
"We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in the previously constructed semi-classical states."

Aastrup and Grimstrup have been pursuing the goal of merging the standard particle model in Connes NCG form, with a variant of canonical LQG. The "spectral triple" is the Connes NCG part---this has to be accommodated on a LQG space.
See their earlier papers for an overview of their project. This appears to be a minor contributory piece of the puzzle.

http://arxiv.org/abs/0911.2391
Wilson loops, geometric operators and fermions in 3d group field theory
R.J. Dowdall
13 pages, many figures
(Submitted on 12 Nov 2009)
"Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler quenched approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory."

Richard Dowdall is at Nottingham, John Barrett's student and recent co-author. I guess this paper fits into the overall spin foam program, and contributes towards inclusion of matter.

 

[John86]

http://arxiv.org/abs/0911.2326
Superfluidity and Stationary Space-Times
Authors: George Chapline (LLNL), Pawel O. Mazur (USC Columbia)
(Submitted on 12 Nov 2009)
Abstract: A connection between superfluidity and gravitation is established for physical stationary gravitational fields. We show that the spinning cosmic string metric describes the gravitational field associated with the single vortex in a superfluid condensate model for space-time outside the vortex core. This metric differs significantly from the usual acoustic metric for the Onsager-Feynman vortex. We also consider the question of what happens when many vortices are present, and show that on large scales a G\"odel-like metric emerges. In both the single and multiple vortex cases the presence of closed time-like curves is attributed to the

 

[John86]

http://arxiv.org/abs/0911.2136
Noncommutative Solitons of Gravity
Authors: Tsuguhiko Asakawa, Shinpei Kobayashi
(Submitted on 11 Nov 2009)
Abstract: We investigate a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only. We found various kinds of nontrivial solutions, by applying a similar technique which was used to seek noncommutative solitons in noncommutative scalar field theories. Some of those solutions correspond to bubbles of spacetimes, or represent dimensional reduction. The solution which interpolates $G_{\mu\nu}=0$ and Minkowski metric is also found. All solutions we obtained are non-perturbative in the noncommutative parameter $\theta$, therefore they are different from solutions found in other contexts of noncommutative theory of gravity and would have a close relation to quantum gravity.

 

[marcus]

http://arxiv.org/abs/0911.2653
Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
Marco Valerio Battisti, Antonino Marciano, Carlo Rovelli
21 pages
(Submitted on 13 Nov 2009)
"We develop the 'triangulated' version of loop quantum cosmology, recently introduced in the literature. We focus on the 'dipole' cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model. We show that the model is rich enough to describe the (anisotropic) Bianchi IX Universe, and give the explicit relation between the Bianchi IX variables and the variables of the model. We discuss the possibility of using this path in order to define the quantization of the Bianchi IX Universe. The model contains more degrees of freedom than Bianchi IX, and therefore captures some inhomogeneous degrees of freedom as well. Inhomogeneous degrees of freedom can be expanded in representations of the SU(2) Bianchi IX isometry group, and the dipole model captures the lowest integer representation of these, connected to hyper-spherical harmonic of angular momentum j=1."


http://arxiv.org/abs/0911.2698
A solution of the strong CP problem a la Peccei-Quinn through the Nieh-Yan modified gravity and cosmological implications
Massimiliano Lattanzi, Simone Mercuri
8 pages, 1 figure
(Submitted on 13 Nov 2009)
"By identifying the recently introduced Barbero-Immirzi field with the QCD axion, the strong CP problem can be solved through the Peccei-Quinn mechanism. A specific energy scale for the Peccei-Quinn symmetry breaking is naturally predicted by this model. This provides a complete dynamical setting to evaluate the contribution of such an axion to the cold dark matter content of the Universe, as function of the initial misalignment angle. Furthermore, a tight upper bound on the tensor-to-scalar ratio production of primordial gravitational waves can be fixed, representing a strong experimental test for this model."

My comment, see footnote [18].

 

[MTd2]

http://arxiv.org/abs/0911.3097

On the spinfoam expansion in cosmology

Carlo Rovelli, Francesca Vidotto
(Submitted on 16 Nov 2009)
We consider the technique introduced in a recent work by Ashtekar, Campiglia and Henderson, which generate a spinfoam-like sum from a Hamiltonian theory. We study the possibility of using it for finding the generalized projector of a constraint on physical states, without first deparametrising the system. We illustrate this technique in the context of a very simple example. We discuss the infinities that appear in the calculation, and argue that they can be appropriately controlled. We apply these ideas to write a spinfoam expansion for the "dipole cosmology".

http://arxiv.org/abs/0911.2761
Phenomenological Quantum Gravity

If the history of science has taught us anything, it's that persistence and creativity makes the once impossible possible. It has long been thought experimental tests of quantum gravity are impossible. But during the last decade, several different approaches have been proposed that allow us to test, if not the fundamental theory of quantum gravity itself, so at least characteristic features this theory can have. For the first time we can probe experimentally domains in which quantum physics and gravity cohabit, in spite of our failure so far to make a convincing marriage of them on a theoretical level.

 

[marcus]

http://arxiv.org/abs/0911.2727
Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity
Alfio Bonanno
28 pages, 6 figures. Invited talk at Workshop on Continuum and Lattice Approaches to Quantum Gravity. Sept. 2008, Brighton UK. To appear in the Proceedings
(Submitted on 13 Nov 2009)
"In recent years it has emerged that the high energy behavior of gravity could be governed by an ultraviolet non-Gaussian fixed point of the (dimensionless) Newton's constant, whose behavior at high energy is thus antiscreened. This phenomenon has several astrophysical implications. In particular in this article recent works on renormalization group improved cosmologies based upon a renormalization group trajectory of Quantum Einstein Gravity with realistic parameter values will be reviewed. It will be argued that quantum effects can account for the entire entropy of the present Universe in the massless sector and give rise to a phase of inflationary expansion. Moreover the prediction for the final state of the black hole evaporation is a Planck size remnant which is formed in an infinite time."
If you choose to print this paper by Bonanno, limit the printing to pages 1-29
After page 29 there is an earlier, imperfect, copy of the paper, which someone neglected to erase when the finished copy was uploaded.


MTd2 has already spotted the next one, so I just make brief mention of it:
http://arxiv.org/abs/0911.2761
Phenomenological Quantum Gravity
Sabine Hossenfelder, Lee Smolin
3 pages. To appear in Physics in Canada

 

[MTd2]

http://arxiv.org/abs/0911.3165

Asymptotically Safe Inflation

Steven Weinberg
(Submitted on 16 Nov 2009)
Inflation is studied in the context of asymptotically safe theories of gravitation. It is found to be possible under several circumstances to have a long period of nearly exponential expansion that eventually comes to an end.

 

[marcus]

http://arxiv.org/abs/0911.3428
On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation
Muxin Han, Thomas Thiemann
43 pages
(Submitted on 17 Nov 2009)
"Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based."

http://arxiv.org/abs/0911.3431
On the Relation between Rigging Inner Product and Master Constraint Direct Integral Decomposition
Muxin Han, Thomas Thiemann
25 pages
(Submitted on 17 Nov 2009)
"Canonical quantisation of constrained systems with first class constraints via Dirac's operator constraint method proceeds by the thory of Rigged Hilbert spaces, sometimes also called Refined Algebraic Quantisation (RAQ). This method can work when the constraints form a Lie algebra. When the constraints only close with nontrivial structure functions, the Rigging map can no longer be defined.
To overcome this obstacle, the Master Constraint Method has been proposed which replaces the individual constraints by a weighted sum of absolute squares of the constraints. Now the direct integral decomposition methods (DID), which are closely related to Rigged Hilbert spaces, become available and have been successfully tested in various situations.
It is relatively straightforward to relate the Rigging Inner Product to the path integral that one obtains via reduced phase space methods. However, for the Master Constraint this is not at all obvious. In this paper we find sufficient conditions under which such a relation can be established. Key to our analysis is the possibility to pass to equivalent, Abelian constraints, at least locally in phase space. Then the Master Constraint DID for those Abelian constraints can be directly related to the Rigging Map and therefore has a path integral formulation."

http://arxiv.org/abs/0911.3432
Path-integral for the Master Constraint of Loop Quantum Gravity
Muxin Han
19 pages
(Submitted on 17 Nov 2009)
"In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint programme. The physical inner product is expressed by using the group averaging technique for a single self-adjoint master constraint operator. By the standard technique of skeletonization and the coherent state path-integral, we derive a path-integral formula from the group averaging for the master constraint operator. Our derivation in the present paper suggests there exists a direct link connecting the canonical Loop quantum gravity with a path-integral quantization or a spin-foam model of General Relativity."

http://arxiv.org/abs/0911.3433
Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
Jonathan Engle, Muxin Han, Thomas Thiemann
26 pages
(Submitted on 17 Nov 2009)
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure" usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed.
In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element.
From this path integral for the Holst formulation of GR we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical LQG and the spin foam approach."

http://arxiv.org/abs/0911.3436
Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
Muxin Han
34 pages
(Submitted on 17 Nov 2009)
"This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory."

http://arxiv.org/abs/0911.3553
The Fine Structure of SU(2) Intertwiners from U(N) Representations
Laurent Freidel, Etera R. Livine
21 pages
(Submitted on 18 Nov 2009)
"In this work we study the Hilbert space space of N-valent SU(2) intertwiners with fixed total spin, which can be identified, at the classical level, with a space of convex polyhedra with N face and fixed total boundary area. We show that this Hilbert space provides, quite remarkably, an irreducible representation of the U(N) group. This gives us therefore a precise identification of U(N) as a group of area preserving diffeomorphism of polyhedral spheres. We use this results to get new closed formulae for the black hole entropy in loop quantum gravity."

 

[MTd2]

http://arxiv.org/abs/0911.3745

Loop quantum gravity and the CMB: toward pre-Big Bounce cosmology
Aurelien Barrau
Comments: Proceedings of the 12th Marcel Grossman Meeting on General Relativity. 3 pages, no figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)
This brief article sums up the possible imprints of loop quantum gravity effects on the cosmological microwave background. We focus on semi-classical terms and show that "Big Bounce" corrections, together with the "pre Big Bounce" state, could modify the observed spectrum.