Linking shape dynamics and loop quantum gravity

TL;DR

This paper derives shape dynamics, a reformulation of general relativity with local scale invariance, using Ashtekar variables and a modified Plebanski action, connecting it to loop quantum gravity frameworks.

Contribution

It introduces a new formulation of shape dynamics based on Ashtekar variables, linking it to loop quantum gravity and providing a novel perspective on gravitational constraints.

Findings

Shape dynamics is shown to be derivable from a modified Plebanski action.

Constraints of shape dynamics are expressed in Ashtekar variables.

The algebra of constraints is reproduced in the new formulation.

Abstract

Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation related to the Ashtekar variables by beginning with a modification of the Plebanski action. The constraints of shape dynamics and their algebra are reproduced in terms of these new variables.