Solving puzzles of spontaneously broken spacetime symmetries

TL;DR

This paper develops a classical analog of the Nambu-Goldstone theorem for spacetime symmetries, providing a counting rule for Nambu-Goldstone fields and clarifying their physical roles, with applications to massive gravity.

Contribution

It introduces a classical framework for counting and characterizing Nambu-Goldstone fields in spontaneously broken spacetime symmetries, including inverse Higgs constraints.

Findings

Only generators acting non-trivially on the vacuum produce independent NG fields.

Generators with trivial action lead to auxiliary fields excluded by inverse Higgs constraints.

Application to massive gravity theories demonstrates the framework's relevance.

Abstract

We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that only those symmetry group generators give rise to independent Nambu-Goldstone fields that act non-trivially on a vacuum at the origin of coordinates. Other generators give rise to auxiliary fields that must be excluded from a theory by the means of inverse Higgs constraints. The physical meaning of the inverse Higgs phenomenon and an application of our results to theories of massive gravity are discussed.