(adsbygoogle = window.adsbygoogle || []).push({}); Sifting the 4th qtr Loop-and-allied QG papers

Here's a tentative lineup of papers that could appear in the 4th quarter MIP poll, in case anyone wants to look it over and comment. As in past years the MIP poll covers Loop-and-allied approaches to Quantum Gravity---our picks as to which paper appearing in the past 3 months you think will prove most valuable to future research.

http://arxiv.org/abs/1112.5104

Quantum Gravity and Renormalization: The Tensor Track

Vincent Rivasseau

(Submitted on 21 Dec 2011)

We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches.

18 pages, 1 figure

http://arxiv.org/abs/1112.2511

q-Deformation of Lorentzian spin foam models

Winston J. Fairbairn, Catherine Meusburger

(Submitted on 12 Dec 2011)

We construct and analyse a quantum deformation of the Lorentzian EPRL model. The model is based on the representation theory of the quantum Lorentz group with real deformation parameter. We give a definition of the quantum EPRL intertwiner, study its convergence and braiding properties and construct an amplitude for the four-simplexes. We find that the resulting model is finite.

12 pages, 2 figures, Proceedings of the 3rd Quantum Gravity and Quantum Geometry School (Zakopane, 2011), to appear in PoS

http://arxiv.org/abs/1112.2390

The geometric role of symmetry breaking in gravity

Derek K. Wise

(Submitted on 11 Dec 2011)

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.

4 pages. Contribution written for proceedings of the conference "Loops 11" (Madrid, May 2011)

http://arxiv.org/abs/1112.1961

Spin Foams and Canonical Quantization

Sergei Alexandrov, Marc Geiller, Karim Noui

(Submitted on 8 Dec 2011)

This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev-Viro spin foam model, and how the Ponzano-Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the four-dimensional case, we recall a Lorentz-covariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.

88 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

http://arxiv.org/abs/1112.0360

Positive cosmological constant in loop quantum cosmology

Tomasz Pawlowski, Abhay Ashtekar

(Submitted on 1 Dec 2011)

The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is surprisingly insensitive to the choice of the self-adjoint extension. This may be a special case of an yet to be discovered general property of a certain class of symmetric operators that fail to be essentially self-adjoint.

36 pages, 6 figures

http://arxiv.org/abs/1111.7195

Spontaneously broken Lorentz symmetry for Hamiltonian gravity

Steffen Gielen, Derek K. Wise

(Submitted on 30 Nov 2011)

In Ashtekar's Hamiltonian formulation of general relativity, and in loop quantum gravity, Lorentz covariance is a subtle issue that has been strongly debated. Maintaining manifest Lorentz covariance seems to require introducing either complex-valued fields or second class constraints, and either option presents a significant obstacle to quantization. After reviewing the sources of difficulty, we present a Lorentz covariant, real formulation free of second class constraints. Rather than a foliation of spacetime, we use a gauge field y, interpreted as a field of observers, to break the SO(3,1) symmetry down to a subgroup SO(3)_{y}. This symmetry breaking plays a role analogous to that in MacDowell-Mansouri gravity, which is based on Cartan geometry, leading us to a picture of gravity as 'Cartan geometrodynamics.' We study both Lorentz gauge transformations and transformations of the observer field to show that the apparent breaking of SO(3,1) to SO(3) is not in conflict with Lorentz covariance.

10 pages

http://arxiv.org/abs/1111.4997

A Renormalizable 4-Dimensional Tensor Field Theory

Joseph Ben Geloun, Vincent Rivasseau

(Submitted on 21 Nov 2011)

We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)^{4}is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the φ^{6}rather than of the φ^{4}type, since two different φ^{6}-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent (∫φ^{2})^{2}term, which can be interpreted as the generation of a scalar matter field out of pure gravity.

41 pages, 9 figures

http://arxiv.org/abs/1111.3695

Is de Sitter space a fermion?

Andrew Randono

(Submitted on 16 Nov 2011)

Following up on a recent model yielding fermionic geometries, I turn to more familiar territory to address the question of statistics in purely geometric theories. Working in the gauge formulation of gravity, where geometry is characterized by a symmetry broken Cartan connection, I give strong evidence to suggest that de Sitter space itself, and a class of de Sitter-like geometries, can be consistently quantized fermionically. Surprisingly, the underlying mathematics is the same as that of the Skyrme model for strongly interacting baryons. This promotes the question "Is geometry bosonic or fermionic?" [ http://arxiv.org/abs/1105.4184 ] beyond the realm of the rhetorical and places it on uncomfortably familiar ground.

15 pages, 4 figures

http://arxiv.org/abs/1111.3535

Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology

Thomas Cailleteau, Jakub Mielczarek, Aurelien Barrau, Julien Grain

(Submitted on 15 Nov 2011)

Holonomy corrections to scalar perturbations are investigated in the loop quantum cosmology framework. Due to the effective approach, modifications of the algebra of constraints generically lead to anomalies. In order to remove those anomalies, counter-terms are introduced. We find a way to explicitly fulfill the conditions for anomaly freedom and we give explicit expressions for the counter-terms. Surprisingly, the "new quantization scheme" naturally arises in this procedure. The gauge invariant variables are found and equations of motion for the anomaly-free scalar perturbations are derived. Finally, some cosmological consequences are discussed qualitatively.

19 pages, 1 figure

http://arxiv.org/abs/1111.2865

A proposed proper EPRL vertex amplitude

Jonathan Engle

(Submitted on 11 Nov 2011)

As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called 'new' spin-foam models mix three of the five sectors of Plebanski theory, only one of which is gravity in the usual sense, and this is the reason for certain 'unwanted' terms in the asymptotics of the EPRL vertex amplitude as calculated by Barrett et al.

In the present paper, an explicit classical discrete condition is derived that isolates the desired gravitational sector, which we call (II+), following other authors. This condition is quantized and used to modify the vertex amplitude, yielding what we call the 'proper EPRL vertex amplitude'. This vertex still depends only on standard SU(2) spin-network data on the boundary, is SU(2) gauge invariant, and is linear in the boundary state, as required. In addition, the asymptotics now consist in the single desired term of the form e^{iSRegge}, and all degenerate configurations are exponentially suppressed.

25 pages

http://arxiv.org/abs/1111.1743

Higher Derivative Gravity from the Universal Renormalization Group Machine

F. Saueressig, K. Groh, S. Rechenberger, O. Zanusso

(Submitted on 7 Nov 2011)

We study the renormalization group flow of higher derivative gravity, utilizing the functional renormalization group equation for the average action. Employing a recently proposed algorithm, termed the universal renormalization group machine, for solving the flow equation, all the universal features of the one-loop beta-functions are recovered. While the universal part of the beta-functions admits two fixed points, we explicitly show that the existence of one of them depends on the choice of regularization scheme, indicating that it is most probably unphysical.

7 pages

http://arxiv.org/abs/1110.6866

Path integral measure and triangulation independence in discrete gravity

Bianca Dittrich, Sebastian Steinhaus

(Submitted on 31 Oct 2011)

A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi-classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D.

36 pages, 7 figures

http://arxiv.org/abs/1110.6150

Regularized Hamiltonians and Spinfoams

Emanuele Alesci

(Submitted on 27 Oct 2011)

We review a recent proposal for the regularization of the scalar constraint of General Relativity in the context of LQG. The resulting constraint presents strengths and weaknesses compared to Thiemann's prescription. The main improvement is that it can generate the 1-4 Pachner moves and its matrix elements contain 15j Wigner symbols, it is therefore compatible with the spinfoam formalism: the drawback is that Thiemann anomaly free proof is spoiled because the nodes that the constraint creates have volume.

4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS)

http://arxiv.org/abs/1110.4833

Continuous formulation of the Loop Quantum Gravity phase space

Laurent Freidel, Marc Geiller, Jonathan Ziprick

(Submitted on 21 Oct 2011)

In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux variables. Our construction shows that the fluxes depend on the three-geometry, but also explicitly on the connection, explaining their non commutativity. It also clearly shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. This allows us to resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since we establish that both geometries belong to the same equivalence class. This finally gives us a clear understanding of the relationship between the piecewise flat spin foam geometries and Regge geometries, which are only piecewise-linear flat: While Regge geometry corresponds to metrics whose curvature is concentrated around straight edges, the loop gravity geometry correspond to metrics whose curvature is concentrated around not necessarily straight edges.

27 pages

http://arxiv.org/abs/1110.3837

Coupling Shape Dynamics to Matter Gives Spacetime

Henrique Gomes, Tim Koslowski

(Submitted on 17 Oct 2011)

Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomporphisms and local spatial conformal transformations. In this paper we extend the construction of Shape Dynamics from pure gravity to gravity-matter systems and find that there is no obstruction for the coupling of gravity to standard matter. We use the matter gravity system to construct a clock and rod model for Shape Dynamics which allows us to recover a spacetime interpretation of Shape Dynamics trajectories.

10 pages

http://arxiv.org/abs/1110.3272

A new Hamiltonian for the Topological BF phase with spinor networks

Valentin Bonzom, Etera R. Livine

(Submitted on 14 Oct 2011)

We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is different from the plaquette operator. Its gauge-theoretical content at the classical level is formulated in terms of spinors. The quantization is performed with Schwinger's bosonic operators on the links of the lattice. In the spin network basis, the quantum Hamiltonian yields a difference equation based on the spin 1/2. In the simplest case, it is identified as a recursion on Wigner 6j-symbols. We also study it in different coherent states representations, and compare with other equations which capture some aspects of this topological phase.

40 pages

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# Sifting the 4th qtr QG papers

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