A shape dynamical approach to holographic renormalization

The European Physical Journal C

Sean Gryb¹  Lee Smolin²  Flavio Mercati²  Henrique Gomes³  Tim Koslowski⁴ 

[1] Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands;Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Nijmegen, The Netherlands;Perimeter Institute for Theoretical Physics, 31 Caroline Street North, N2L 2Y5, Waterloo, ON, Canada;University of California at Davis, One Shields Avenue, 95616, Davis, CA, USA;University of New Brunswick, E3B 5A3, Fredericton, NB, Canada;

关键词: Gauge Symmetry;    Conformal Field Theory;    Semiclassical Limit;    Hamiltonian Constraint;    Holographic Renormalization;   

DOI  :  10.1140/epjc/s10052-014-3238-z

来源: Springer

【 摘 要 】

We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk–bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk–bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities.

【 授权许可】

CC BY