Unstable Nambu-Goldstone modes

TL;DR

This paper provides a universal framework using symmetry algebra to understand the instability of Nambu-Goldstone modes in various physical contexts involving background fields, revealing new instability phenomena.

Contribution

It introduces a unified algebraic approach to describe and count unstable NG modes for 0-form and higher-form symmetries, including new examples.

Findings

Universal description of NG mode instabilities via symmetry algebra

A counting rule for unstable NG modes based on correlation functions

Identification of a new instability example in a specific symmetry breaking scenario

Abstract

Nambu-Goldstone (NG) modes for 0-form and higher-form symmetries can become unstable in the presence of background fields. Examples include the instability of a photon with a time-dependent axion background or with a chirality imbalance, known as the chiral plasma instability, and the instability of a dynamical axion with a background electric field. We show that all these phenomena can be universally described by a symmetry algebra for 0-form and higher-form symmetries. We prove a counting rule for the number of unstable NG modes in terms of correlation functions of broken symmetry generators. Based on our unified description, we further give a simple new example where one of the NG modes associated with the spontaneous 0-form symmetry breaking $U(1) \times U(1) \to \{1\}$ becomes unstable.