Unstable Nambu-Goldstone modes

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)×U(1)→1 becomes unstable.