Sound as a gauge theory and its infrared triangle

Abstract

Over the last few decades, a rich structure has been uncovered in the infrared sector of various field theories. This mostly comes through the connections between memory effects, asymptotic symmetries, and soft theorems (the ``infrared triangle''), which have been explored in much depth within 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. We then 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. Standard techniques can then be used 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 an example of an infrared triangle in a condensed matter system and provides new pathways to the experimental detection of memory effects.