Spontaneous Symmetry Probing

TL;DR

This paper introduces the concept of spontaneous symmetry probing (SSP) in relativistic quantum field theories, analyzing the behavior of symmetry-breaking states and their associated Goldstone modes, with potential implications for cosmology.

Contribution

It formalizes SSP, proves properties of fluctuations around SSP states, and explores the gap formation in non-Abelian symmetry groups, extending understanding of symmetry breaking dynamics.

Findings

Fluctuations around SSP states have time-independent Lagrangians.

A gapless Goldstone mode always exists in the direction of motion in field space.

Non-Abelian symmetries lead to gapped Goldstone bosons proportional to the SSP state's speed.

Abstract

For relativistic quantum field theories, we consider Lorentz breaking, spatially homogeneous field configurations or states that evolve in time along a symmetry direction. We dub this situation "spontaneous symmetry probing" (SSP). We mainly focus on internal symmetries, i.e. on symmetries that commute with the Poincare group. We prove that the fluctuations around SSP states have a Lagrangian that is explicitly time independent, and we provide the field space parameterization that makes this manifest. We show that there is always a gapless Goldstone excitation that perturbs the system in the direction of motion in field space. Perhaps more interestingly, we show that if such a direction is part of a non-Abelian group of symmetries, the Goldstone bosons associated with spontaneously broken generators that do not commute with the SSP one acquire a gap, proportional to the SSP state's "speed". We outline possible applications of this formalism to inflationary cosmology.