Sound as a gauge theory and its infrared triangle

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.

💡 Research Summary

The paper “Sound as a gauge theory and its infrared triangle” establishes a complete infrared‑triangle structure—memory effect, asymptotic symmetries, and soft theorems—for linear acoustic perturbations in a barotropic, irrotational fluid. The authors begin by linearizing the continuity and Euler equations around a homogeneous, quiescent background, introducing a scalar velocity potential ϕ that satisfies the inhomogeneous wave equation (-\frac{1}{c^{2}}\partial_{t}^{2}\phi+\nabla^{2}\phi = q). The source term q models time‑dependent boundary motions (e.g., a pulsating sphere) via the method of images, turning a moving surface into an equivalent distribution of “image” volume sources. Solving the wave equation with the retarded Green’s function yields a closed‑form expression for ϕ; integrating the resulting velocity field shows that after the source is switched off the fluid particles retain a permanent displacement. This is identified as the acoustic memory effect, directly analogous to the gravitational wave memory first described by Zel’dovich and Polnarev.

The central innovation is to recast the scalar potential ϕ as the gauge potential of a Kalb‑Ramond two‑form field B_{\mu\nu}. The field strength H = dB is a three‑form, invariant under the gauge transformation B → B + dΛ with Λ a one‑form. This reformulation places linear sound within the well‑studied framework of p‑form electrodynamics (p = 2), allowing the authors to import the machinery of asymptotic analysis and large‑gauge transformations. By examining the behavior of B_{\mu\nu} at future null infinity (\mathscr{I}^{+}), they identify a set of residual gauge parameters that survive at infinity; these parameters constitute an infinite‑dimensional asymptotic symmetry group, directly mirroring the Bondi‑Metzner‑Sachs (BMS) symmetries of gravity and the large‑U(1) symmetries of electromagnetism.

To connect the memory effect with these asymptotic symmetries, the authors compute the change in the boundary value of B_{\mu\nu} induced by the source q. They demonstrate that the permanent shift in the fluid particle positions is precisely equal to the change in the large‑gauge parameter, establishing a one‑to‑one correspondence between acoustic memory and a specific element of the asymptotic symmetry group.

The soft‑theorem side of the triangle is addressed by considering the low‑frequency limit of acoustic radiation. In the ω → 0 regime, the emitted “soft phonon” amplitude obeys a Ward identity that follows from the conservation of the asymptotic charge associated with the large‑gauge transformation. This identity reproduces the familiar soft‑theorem structure known from graviton and photon scattering, but its physical interpretation is now the relationship between a low‑frequency acoustic pulse and the induced permanent fluid displacement.

The paper also discusses experimental implications. Because the source term q can be engineered in the laboratory (e.g., by driving a sphere or a membrane with a prescribed time profile), one can deliberately excite specific large‑gauge modes and measure the resulting memory using particle‑tracking velocimetry or laser Doppler anemometry. The authors argue that the acoustic infrared triangle provides a realistic platform for testing concepts that have so far been confined to high‑energy theory.

Finally, the authors place their work in context with prior studies of analogue gravity, noting that while previous works have used scalar field analogues of gravity, this is the first to employ a two‑form gauge field to describe sound, thereby exposing the full infrared‑triangle structure in a condensed‑matter system. The appendix reviews the necessary differential‑form and de Rham cohomology background. Overall, the study offers a novel theoretical bridge between acoustic physics and modern infrared quantum‑field‑theoretic ideas, opening new avenues for both theoretical exploration and experimental verification.