Shape Dynamics and Effective Field Theory

Abstract

Shape Dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable form classical General Relativity. If taken seriously, it suggests that the spacetime--geometry picture that underlies General Relativity can be replaced by a picture based on spatial conformal geometry. This classically well understood trading of gauge symmetries opens new conceptual avenues in many approaches to quantum gravity. I focus on the general implications for quantum gravity and effective field theory and consider the application of the Shape Dynamics picture in the exact renormalization group approaches to gravity, loop- and polymer- quantization approaches to gravity and low energy effective field theories. I also discuss the interpretation of known results through in the Shape Dynamics picture, in particular holographic renormalization and the problem of time in canonical quantum gravity.

56 pages, LaTex, 1 figure

References in corpus (2)

• Quantum Gravity at a Lifshitz Point
• Einstein gravity as a 3D conformally invariant theory

Cited by in corpus (6)

• A Shape Dynamical Approach to Holographic Renormalization
• Conformal geometrodynamics regained: gravity from duality
• Quantum gravity in timeless configuration space
• Shape Dynamical Loop Gravity from a Conformal Immirzi Parameter
• Semi-classical locality for the non-relativistic path integral in configuration space
• A first look at Weyl anomalies in shape dynamics