Construction of higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theory

TL;DR

This paper develops a systematic approach to constructing higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theories, focusing on conservation laws and their implications for phenomenology.

Contribution

It provides a comprehensive method to derive all relevant higher-order terms in the presence of spontaneous diffeomorphism and Lorentz symmetry breaking, including their constraints.

Findings

All cubic order terms for two-tensor couplings are derived.

Diffeomorphism symmetry constrains the decoupling of tensor and metric fluctuations.

Special cases allow for decoupling at quadratic order.

Abstract

We examine the basic conservation laws for diffeomorphism symmetry in the context of spontaneous diffeomorphism and local Lorentz-symmetry breaking. The conservation laws are used as constraints on a generic series of terms in an expansion around a flat background. We find all such terms for a two-tensor coupling to cubic order in the metric and tensor field fluctuations. The results are presented in a form that can be used for phenomenological calculations. One key result is that if we preserve the underlying diffeomorphism symmetry in a spontaneous-symmetry breaking scenario, one cannot decouple the two-tensor fluctuations from the metric fluctuations at the level of the action, except in special cases of the quadratic actions.