Features of Spacetime-Symmetry Breaking and the Standard-Model Extension in Riemann-Cartan Geometry

TL;DR

This paper reviews the theoretical aspects of spacetime-symmetry breaking within the Standard-Model Extension in Riemann-Cartan geometry, highlighting differences between spontaneous and explicit breaking and proposing a modified framework for gravity theories.

Contribution

It provides a detailed analysis of symmetry breaking in Riemann-Cartan geometry and introduces a modified SME framework for explicit symmetry breaking in gravity.

Findings

Differences between spontaneous and explicit breaking clarified.

Modified SME suitable for explicit breaking in gravity developed.

Insights into new geometries beyond Riemann-Cartan obtained.

Abstract

For over two decades, the gravity sector of the Standard-Model Extension (SME) has served as a phenomenological framework for testing spacetime symmetry breaking in the presence of gravity. During this time, various theoretical features have been examined in greater detail and some refinements have been made. In particular, differences between spontaneous and explicit breaking of diffeomorphisms, local translations, and local Lorentz transformations in Riemann-Cartan geometry, as well as their corresponding consistency issues with geometric and mathematical identities, have been probed more deeply. This has led to a modified version of the SME being developed that is suitable for investigating explicit breaking in gravity theories, which can be used as well to search for new geometries that go beyond Riemann-Cartan. A selective overview of some of these features is presented here.