Effective Theory Approach to the Spontaneous Breakdown of Lorentz Invariance

TL;DR

This paper develops a formalism to describe theories with spontaneously broken Lorentz invariance using an extended coset construction, enabling analysis of low-energy effective actions without specifying the breaking mechanism.

Contribution

It generalizes the coset construction to Lorentz symmetry breaking, providing a systematic way to derive effective Lagrangians in flat and covariant settings.

Findings

Constructed the most general effective Lagrangian for broken Lorentz symmetry.

Showed that Einstein-aether theory arises as a special case.

Provided a framework for analyzing Lorentz symmetry breaking effects.

Abstract

We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective Lagrangian in which Lorentz invariance is non-linearly realized, and to explore the consequences of broken Lorentz symmetry without having to make any assumptions about the mechanism that triggers the breaking. We carry out the construction both in flat space, in which the Lorentz group is a global spacetime symmetry, and in a generally covariant theory, in which the Lorentz group can be treated as a local internal symmetry. As an illustration of this formalism, we construct the most general effective field theory in which the rotation group remains unbroken, and show that the latter is just the Einstein-aether theory.