How to construct diffeomorphism symmetry on the lattice

TL;DR

This paper develops a perturbative framework to construct lattice discretizations that preserve diffeomorphism symmetry, which is typically broken during discretization of general relativity, enabling better understanding of gauge invariance in discrete models.

Contribution

It introduces a perturbative approach to achieve exact diffeomorphism symmetry on the lattice, along with consistency conditions for preserving gauge invariance.

Findings

Framework for constructing diffeomorphism-invariant discretizations

Identification of consistency conditions for gauge symmetry preservation

Structural insights into diffeomorphism invariant discretizations

Abstract

Diffeomorphism symmetry, the fundamental invariance of general relativity, is generically broken under discretization. After discussing the meaning and implications of diffeomorphism symmetry in the discrete, in particular for the continuum limit, we introduce a perturbative framework to construct discretizations with an exact notion of diffeomorphism symmetry. We will see that for such a perturbative framework consistency conditions need to be satisfied which enforce the preservation of the gauge symmetry to the perturbative order under discussion. These consistency conditions will allow structural investigations of diffeomorphism invariant discretizations.