Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Sound as a gauge theory and its infrared triangle

Níckolas de Aguiar Alves, André G. S. Landulfo

TL;DR

This work shows that acoustic perturbations in a simple fluid setting exhibit an infrared triangle analogous to high-energy theories: memory effects, asymptotic symmetries, and soft theorems. By reformulating linear acoustics as a Kalb-Ramond two-form gauge theory, the authors connect lasting fluid displacements to large gauge transformations and discuss how a scalar soft theorem can encode the memory. They provide a Maxwell-influenced case study to illustrate the memory–symmetry–soft theorem trio and extend the framework to an acoustic two-form formalism, highlighting the role of image sources in modeling boundary conditions. The results propose a concrete, experimentally accessible platform for probing infrared structure in a condensed-matter context and motivate extensions to nonlinear memory and phonon-soft theorems.

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.

Sound as a gauge theory and its infrared triangle

TL;DR

This work shows that acoustic perturbations in a simple fluid setting exhibit an infrared triangle analogous to high-energy theories: memory effects, asymptotic symmetries, and soft theorems. By reformulating linear acoustics as a Kalb-Ramond two-form gauge theory, the authors connect lasting fluid displacements to large gauge transformations and discuss how a scalar soft theorem can encode the memory. They provide a Maxwell-influenced case study to illustrate the memory–symmetry–soft theorem trio and extend the framework to an acoustic two-form formalism, highlighting the role of image sources in modeling boundary conditions. The results propose a concrete, experimentally accessible platform for probing infrared structure in a condensed-matter context and motivate extensions to nonlinear memory and phonon-soft theorems.

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.

Paper Structure

This paper contains 18 sections, 195 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Linear Sound and Acoustic Memory
  3. Linear acoustic perturbations and sources
  4. Acoustic memory
  5. Sound as a Gauge Theory
  6. Gauge potential
  7. Image sources
  8. Case Study: The Maxwell Infrared Triangle
  9. The memory effect
  10. The asymptotic symmetries
  11. The soft theorem
  12. Memory in the Two-Form Formalism
  13. Asymptotic Symmetries
  14. Soft Theorem
  15. Discussion
  16. ...and 3 more sections

Figures (1)

  • Figure 1: Left: a moving surface, such as a sphere with oscillating radius, disturbs the fluid around it and generated sound waves. Right: using the method of images, we can understand the sound waves as being generated by "image sources" inside the surface. We solve the problem in a larger region, with the understanding that the interior of the original surface (shaded region) is to be considered unphysical.