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Title: Conformal geometrodynamics regained: Gravity from duality

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 355; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-05-05 03:01:20; Journal ID: ISSN 0003-4916
Country of Publication:
United States

Citation Formats

Gomes, Henrique. Conformal geometrodynamics regained: Gravity from duality. United States: N. p., 2015. Web. doi:10.1016/j.aop.2015.02.017.
Gomes, Henrique. Conformal geometrodynamics regained: Gravity from duality. United States. doi:10.1016/j.aop.2015.02.017.
Gomes, Henrique. 2015. "Conformal geometrodynamics regained: Gravity from duality". United States. doi:10.1016/j.aop.2015.02.017.
title = {Conformal geometrodynamics regained: Gravity from duality},
author = {Gomes, Henrique},
abstractNote = {},
doi = {10.1016/j.aop.2015.02.017},
journal = {Annals of Physics},
number = C,
volume = 355,
place = {United States},
year = 2015,
month = 4

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.aop.2015.02.017

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Cited by: 6works
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  • There exist several ways of constructing general relativity from ‘first principles’: Einstein’s original derivation, Lovelock’s results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and Hojman–Kuchař-Teitelboim’s derivation of the Hamiltonian form of the theory from the symmetries of space–time, to name a few. Here I propose a different set of first principles to obtain general relativity in the canonical Hamiltonian framework without presupposing space–time in any way. I first require consistent propagation of scalar spatially covariant constraints (in the Dirac picture of constrained systems). I find that up to a certain order in derivatives (four spatialmore » and two temporal), there are large families of such consistently propagated constraints. Then I look for pairs of such constraints that can gauge-fix each other and form a theory with two dynamical degrees of freedom per space point. This demand singles out the ADM Hamiltonian either in (i) CMC gauge, with arbitrary (finite, non-zero) speed of light, and an extra term linear in York time, or (ii) a gauge where the Hubble parameter is conformally harmonic.« less
  • Einsteinian geometrodynamics is the only (time-reversible) canonical representation of the set of generators of deformations of a spacelike hypersurface embedded in a Riemannian spacetime, if the intrinsic metric of that hypersurface and a conjugate momentum are the sole canonical variables. (AIP)
  • The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the Arnowitt-Deser-Misner (ADM) phase space for canonical general relativity to that consisting of York's mean exterior curvature time, conformal three-metric and their momenta. Accordingly, an additional constraint is introduced, called the conformal constraint. In terms of the new canonical variables, a diffeomorphism constraint is derived from the original momentum constraint. The Hamiltonian constraint then takes a new form. It turns out to be the sum of an expression that previously appeared in the literature and extra terms quadratic in the conformal constraint. The complete set of themore » conformal, diffeomorphism and Hamiltonian constraints are shown to be of first class through the explicit construction of their Poisson brackets. The extended algebra of constraints has as subalgebras the Dirac algebra for the deformations and Lie algebra for the conformorphism transformations of the spatial hypersurface. This is followed by a discussion of potential implications of the presented theory on the Dirac constraint quantization of general relativity. An argument is made to support the use of the York time in formulating the unitary functional evolution of quantum gravity. Finally, the prospect of future work is briefly outlined.« less
  • The deconfined quantum critical point of a two-dimensional SU(N) antiferromagnet is governed by an Abelian Higgs model in d=2+1 spacetime dimensions featuring N complex scalar fields. In this context, we derive for 2{<=}d{<=}4 an exact formula for the central charge of the U(1) current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for d=2+1. In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for themore » charge susceptibility in the large N limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in the absence of supersymmetry.« less
  • We use gauge/gravity duality to study the thermodynamics of a field theory with asymptotic freedom in the ultraviolet and a fixed point in the infrared. We find a high temperature quark-gluon phase and a low T conformal unparticle phase. The phase transition between the phases is of first order or continuous, depending on the ratio of the radii of asymptotic anti-de Sitter spaces at T=0 and T={infinity}. This is a prediction from a model of gauge/gravity duality, not yet verified on the field theory side.