Simplest phonons and pseudo-phonons in field theory

TL;DR

This paper investigates how Nambu-Goldstone modes, specifically phonons and pseudo-phonons, emerge from broken translation symmetry in field theory, analyzing simple models and their mass behaviors under explicit breaking.

Contribution

It introduces the simplest models with gradient Mexican hats to study space-dependent order parameters and connects these findings to holographic Q-lattices.

Findings

Massless phonons arise from spontaneous translation symmetry breaking.

Pseudo-phonon masses follow Gell Mann-Oakes-Renner relations.

Analysis of simple theories with space-dependent order parameters.

Abstract

We study the emergence of Nambu-Goldstone modes due to broken translation symmetry in field theory. Purely spontaneous breaking yields a massless phonon which develops a mass upon introducing a perturbative explicit breaking. The pseudo-phonon mass agrees with Gell Mann-Oakes-Renner relations. We analyze the simplest possible theories featuring gradient Mexican hats and describing space-dependent order parameters. We comment on homogeneous translation breaking and the connections with holographic Q-lattices.