Breaking and restoring of diffeomorphism symmetry in discrete gravity

TL;DR

This paper explores how diffeomorphism symmetry is affected by discretization in gravity theories, examining the potential for perfect actions to restore symmetry and discussing implications for observables and canonical formulation.

Contribution

It reviews initial approaches to constructing discrete gravity actions that preserve diffeomorphism symmetry exactly, addressing a key challenge in discrete quantum gravity.

Findings

Discretization typically breaks diffeomorphism symmetry.

Perfect actions may restore exact symmetry in discrete gravity.

Implications for observables and canonical formulation are discussed.

Abstract

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so--called perfect actions, with exact symmetries and we will review first steps towards this end.