Shape Dynamics and Effective Field Theory

TL;DR

Shape Dynamics offers an alternative gauge theory perspective to General Relativity, emphasizing spatial conformal geometry, with significant implications for quantum gravity, effective field theories, and the interpretation of holography and time in quantum gravity.

Contribution

This paper explores the conceptual and practical implications of Shape Dynamics for quantum gravity and effective field theories, proposing a shift from spacetime to spatial conformal geometry.

Findings

Shape Dynamics is classically equivalent to General Relativity.

It provides new insights into holographic renormalization.

It offers a novel perspective on the problem of time in quantum gravity.

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.