http://arxiv.org/abs/1312.7797
Quantum indeterminacy in local measurement of cosmic expansion
Craig J. Hogan
(Submitted on 30 Dec 2013)
For a system of two small bodies in an expanding universe, bounds on mass and separation are estimated, from standard gravity and quantum mechanics, such that both their gravity and the process of quantum measurement affect their motion less than the cosmic expansion does. It is shown that such a direct local measurement of cosmic expansion or acceleration at rate H is only possible, even in principle, in a region of size greater than H −3/5 in Planck units, or about 60 meters in the current universe, a new scale that defines a boundary between quantum and classical expansion. A generalization to spatially extended linear density perturbations shows the same scale. Matching vacuum energy or directional information in localized field states to gravity on this system length scale yields a particle mass scale of H 3/10 , or about 7 GeV today. Possible connections of cosmic acceleration with the QCD vacuum are discussed.
http://arxiv.org/abs/1312.7798
Directional Entanglement of Quantum Fields with Quantum Geometry
Craig J. Hogan
(Submitted on 30 Dec 2013)
Using transversely localized solutions of the relativistic wave equation, the path of a massless particle with wavelength λ that travels a distance z is shown to have a wave function with indeterminacy in direction given by the diffraction scale, ⟨Δθ 2 ⟩>2 √ λ/πz . It is conjectured that the spatial structure of quantum field states is influenced by quantum directional indeterminacy of geometry set by the Planck length, l P . Entanglement of field and geometry states is described in the small angle approximation. The entanglement has almost no effect on local measurements, microscopic particle interactions, or measurements of propagating states that depend only on longitudinal coordinates, but significantly alters field states in systems larger than ≈λ 2 /l P that depend on transverse coordinates or direction. It reduces the information content of fields in large systems, consistent with holographic bounds from gravitation theory, and may lead to quantum-geometrical directional fluctuations of massive bodies detectable with interferometers. Possible connections are discussed with field vacuum energy, black hole information, and inflationary fluctuations.
http://arxiv.org/abs/1312.7767
Quantization and fixed points of non-integrable Weyl theory
Carlo Pagani, Roberto Percacci
(Submitted on 30 Dec 2013)
We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations. We quantize the theory by suitably defining renormalization group flows that describe the integration of successive momentum shells, in such a way that Weyl--invariance is maintained in the flow. When the gauge fields are massless the theory has, in addition to Weyl invariance, an abelian gauge symmetry. According to the definition of the cutoff, the flow can break or preserve this extended symmetry. We discuss the fixed points of these flows.
http://arxiv.org/abs/1312.7842
Twistors and antipodes in de Sitter space
Yasha Neiman
(Submitted on 30 Dec 2013)
We develop the basics of twistor theory in de Sitter space, up to the Penrose transform for free massless fields. We treat de Sitter space as fundamental, as one does for Minkowski space in conventional introductions to twistor theory. This involves viewing twistors as spinors of the de Sitter group SO(4,1). When attached to a spacetime point, such a twistor can be reinterpreted as a local SO(3,1) Dirac spinor. Our approach highlights the antipodal map in de Sitter space, which gives rise to doublings in the standard relations between twistors and spacetime. In particular, one can generate a field with both handedness signs from a single twistor function. Such fields naturally live on antipodally-identified de Sitter space dS_4/Z_2, which has been put forward as the ideal laboratory for quantum gravity with positive cosmological constant.
http://arxiv.org/abs/1312.7856
Gravitation from Entanglement in Holographic CFTs
Thomas Faulkner, Monica Guica, Thomas Hartman, Robert C. Myers, Mark Van Raamsdonk(Submitted on 30 Dec 2013)
Entanglement entropy obeys a 'first law', an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S=A/(4G N ) , we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.
http://arxiv.org/abs/1312.7878
Into the Amplituhedron
Nima Arkani-Hamed, Jaroslav Trnka
(Submitted on 30 Dec 2013)
We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4 SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.
http://arxiv.org/abs/1312.7828
First order gravity: Actions, topological terms and boundaries
Alejandro Corichi, Irais Rubalcava, Tatjana Vukasinac
(Submitted on 30 Dec 2013)
We consider first order gravity in four dimensions. This means that the fundamental variables are a tetrad e and a SO(3,1) connection ω . We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein-Hilbert term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle also implies adding additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. We consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. For our analysis we employ the covariant Hamiltonian formalism where the phase space Γ is given by solutions to the equation of motion. For each of the possible terms contributing to the action we study the well posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. While some of the results are not new, we have several results that are novel and have not appeared elsewhere. Furthermore, we point out and clarify some issues that have not been clearly understood in the literature. The aim of the paper is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical.
