Gravity, Lorentz Violation, and the Standard Model

TL;DR

This paper develops a framework for incorporating Lorentz and CPT violation into gravitational theories using Riemann-Cartan geometries, extending the Standard-Model Extension to include gravity and analyzing the implications of explicit and spontaneous symmetry breaking.

Contribution

It formulates the SME in Riemann-Cartan spacetimes, constructs leading-order terms involving operators of mass dimension three and four, and discusses the compatibility of Lorentz violation with gravity.

Findings

Explicit Lorentz breaking is incompatible with Riemann-Cartan geometries.

Spontaneous Lorentz breaking can evade compatibility issues.

Provides the leading-order gravitational SME action terms.

Abstract

The role of the gravitational sector in the Lorentz- and CPT-violating Standard-Model Extension (SME) is studied. A framework is developed for addressing this topic in the context of Riemann-Cartan spacetimes, which include as limiting cases the usual Riemann and Minkowski geometries. The methodology is first illustrated in the context of the QED extension in a Riemann-Cartan background. The full SME in this background is then considered, and the leading-order terms in the SME action involving operators of mass dimension three and four are constructed. The incorporation of arbitrary Lorentz and CPT violation into general relativity and other theories of gravity based on Riemann-Cartan geometries is discussed. The dominant terms in the effective low-energy action for the gravitational sector are provided, thereby completing the formulation of the leading-order terms in the SME with gravity. Explicit Lorentz symmetry breaking is found to be incompatible with generic Riemann-Cartan geometries, but spontaneous Lorentz breaking evades this difficulty.