Symmetries in the SME gravity sector: A study in the first-order formalism

TL;DR

This paper presents a method to identify symmetries in first-order formalism gravity theories, applies it to the SME gravity sector, and clarifies the relationship between Lorentz violation and diffeomorphism invariance.

Contribution

It introduces a new method for finding symmetries in first-order gravity theories and applies it to the SME gravity sector, clarifying Lorentz violation implications.

Findings

No inconsistencies with explicit Lorentz violation.

Lorentz violation is compatible with diffeomorphism invariance.

The method effectively identifies symmetries in the SME gravity sector.

Abstract

A method to find the symmetries of a theory in the first order formalism of gravity is presented. This method is applied to the minimal gravity sector of the Standard Model Extension. It is argued that no inconsistencies arise when Lorentz violation is explicit and the relation between Lorentz violation and invariance under (active) diffeomorphisms is clearly exposed.