Massive Nambu-Goldstone Bosons

TL;DR

This paper explores the existence, counting, and effective description of massive Nambu-Goldstone bosons across various physical systems, extending previous findings to a broader context.

Contribution

It generalizes the phenomenon of massive Nambu-Goldstone bosons, provides a counting rule, and constructs an effective Lagrangian for their dynamics.

Findings

Massive Nambu-Goldstone bosons exist in diverse systems.

A counting rule for these modes is established.

An effective Lagrangian describing their behavior is developed.

Abstract

Nicolis and Piazza have recently pointed out the existence of Nambu-Goldstone-like excitations in relativistic systems at finite density, whose gap is exactly determined by the chemical potential and the symmetry algebra. We show that the phenomenon is much more general than anticipated and demonstrate the presence of such modes in a number of systems from (anti)ferromagnets in magnetic field to superfluid phases of quantum chromodynamics. Furthermore, we prove a counting rule for these massive Nambu-Goldstone bosons and construct a low-energy effective Lagrangian that captures their dynamics.