Sound as a gauge theory and its infrared triangle

TL;DR

This paper demonstrates that sound in fluid dynamics can be described as a gauge theory, revealing an infrared triangle analogous to high-energy physics, and suggests new ways to detect memory effects experimentally.

Contribution

It introduces a gauge-theoretic formulation of linear sound using a Kalb-Ramond field, establishing an infrared triangle in a condensed matter context.

Findings

Sound admits an infrared triangle with memory effects, asymptotic symmetries, and soft theorems.

Linear perturbations of fluid dynamics can be expressed as a gauge theory using a two-form potential.

This framework opens new experimental pathways to observe memory effects in acoustics.

Abstract

Over the last few decades, there has been a considerable interest on the infrared behavior of various field theories. In particular, the connections between memory effects, asymptotic symmetries, and soft theorems (the ``infrared triangle'') have been explored in much depth within the context of high-energy physics. In this paper, we show how sound also admits an infrared triangle. We consider the linear perturbations of the Euler equations for a barotropic and irrotational fluid and show how low-frequency changes in an acoustic source can lead to lasting displacements of fluid particles. We proceed to write these linear perturbations in terms of a two-form potential -- a Kalb--Ramond field, in the high-energy physics terminology. This phrases linear sound as a gauge theory and thus allows the use of standard techniques to probe the infrared structure of acoustics. We show how the memory effect relates to asymptotic symmetries in this dual formulation, and comment on how these notions can be connected to soft theorems. This exhibits the first example of an infrared triangle in a condensed matter system and provides new pathways to the experimental detection of memory effects.