Phases of Pseudo-Nambu-Goldstone Bosons

TL;DR

This paper investigates the vacuum dynamics of pseudo-Nambu-Goldstone bosons arising from $SO(N+1) ightarrow SO(N)$ symmetry breaking, revealing novel vacuum transitions with potential phenomenological implications, including gravitational wave signals.

Contribution

It identifies and analyzes new vacuum transition phenomena in pNGBs, especially under thermal and supercooled conditions, expanding understanding of their phase structure and observable effects.

Findings

Weak first-order thermal vacuum transition.

Strong first-order supercooled vacuum transition with gravitational wave signals.

Explicit symmetry breaking influences vacuum transition types.

Abstract

We study the vacuum dynamics of pseudo-Nambu-Goldstone bosons (pNGBs) for $SO(N+1) \rightarrow SO(N)$ spontaneous and explicit symmetry breaking. We determine the magnitude of explicit symmetry breaking consistent with an EFT description of the effective potential at zero and finite temperatures. We expose and clarify novel additional vacuum transitions that can arise for generic pNGBs below the initial scale of $SO(N+1) \rightarrow SO(N)$ spontaneous symmetry breaking, which may have phenomenological relevance. In this respect, two phenomenological scenarios are analyzed: thermal and supercooled dark sector pNGBs. In the thermal scenario the vacuum transition is first-order but very weak. For a supercooled dark sector we find that, depending on the sign of the explicit symmetry breaking, one can have a symmetry-restoring vacuum transition $SO(N-1) \rightarrow SO(N)$ which can be strongly first-order, with a detectable stochastic gravitational wave background signal.