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Linear sound waves exhibit the full infrared triangle—memory, asymptotic symmetries, and soft theorems—previously associated with gravity and electromagnetism.

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2026-08-03 16:00 UTC pith:GDKYRN5B

load-bearing objection Acoustic memory and two-form asymptotic symmetries are derived cleanly; the claimed infrared triangle has a sketched soft-theorem corner, so the triangle is not fully established. the 2 major comments →

arxiv 2512.15796 v2 pith:GDKYRN5B submitted 2025-12-16 hep-th gr-qc

Sound as a gauge theory and its infrared triangle

N\'ickolas de Aguiar Alves , Andr\'e G. S. Landulfo This is my paper
classification hep-th gr-qc
keywords infrared triangleacoustic memoryKalb-Ramond fieldtwo-form gauge theoryasymptotic symmetriessoft theoremslinearized fluid dynamicswave equation memory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that sound, not just gravity and electrodynamics, exhibits the full infrared triangle: a memory effect, asymptotic symmetries, and soft theorems that are three views of the same long-wavelength structure. It shows low-frequency changes in an acoustic source leave a lasting displacement of fluid particles, rewrites linearized acoustics as a two-form gauge theory, and connects the resulting large gauge transformations to both the memory effect and a scalar soft theorem. If correct, it means the infrared triangle is a general property of four-dimensional wave equations, not an exotic high-energy phenomenon, and brings memory effects within reach of tabletop fluid experiments.

Core claim

The paper shows that linear perturbations of an inviscid, irrotational, barotropic fluid obey the same wave physics that, in gravity and electrodynamics, produces an infrared triangle. In the radiation zone the acoustic perturbation is a closed three-form H whose Hodge dual is also closed, so the theory becomes two-form (Kalb-Ramond) gauge theory. A low-frequency change in a source leaves a permanent displacement of fluid particles at order 1/r; the associated memory two-form decomposes on the sphere into an exact piece (a large gauge transformation) and a harmonic monopole piece (not a large gauge transformation). With pointlike image sources modeled by a sonic Lorentz factor, the memory ef

What carries the argument

The central object is the two-form potential B with field strength H = dB, introduced so that linearized acoustics becomes a p-form gauge theory (a Kalb-Ramond field). The argument runs on the de Rham cohomology of the radiation zone R^2×S^2: closed one-forms and three-forms are exact there, so the scalar phonon field and the gauge potential both exist, while the sphere's unique nontrivial two-form cohomology class produces the harmonic (monopole) memory piece. The memory tensor Δ_AB = 2D_[A C_B] + C ε_AB is the key identity, splitting the memory into a large gauge transformation (exact part) and an irreducible topological piece (harmonic part).

Load-bearing premise

The soft-theorem corner rests on treating acoustic sources as point particles with a 'sonic' Lorentz factor—a modeling choice the paper admits redefines the meaning of 'monopole'; reject that model and the triangle is reduced to the memory and symmetry corners.

What would settle it

A tabletop test: drive a small sphere with a prescribed volume change that ramps up and then stays constant, and measure the displacement of tracer particles at several radii. The central claim predicts a lasting radial displacement scaling as 1/r with amplitude ΔQ/(4π c); if the displacement instead decays after the ramp, or scales differently with r, the acoustic memory claim fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Acoustic memory can in principle be measured in a lab: a pulsating or expanding source that changes its volume flux over a finite interval should leave tracer particles permanently displaced by ΔQ/(4π c r) in the radial direction.
  • The asymptotic-symmetry corner of the triangle holds for sound: leading-order residual gauge transformations of the two-form description, not vanishing at infinity, capture exactly the long-distance memory (except for the monopole piece).
  • The soft-theorem corner, if the point-source model is accepted, gives a Braginsky-Thorne-like formula for acoustic memory in terms of ingoing and outgoing constant-monopole sources.
  • The monopole contribution to acoustic memory is harmonic on the sphere and cannot be written as a large gauge transformation—an analogue of the non-linear memory effects found in gravity.
  • The infrared triangle is not restricted to relativistic fundamental theories; it appears in ordinary fluid mechanics, suggesting analogous triangles in other effective field theories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the memory claim is right, a deformable bubble or synthetic jet provides a tabletop test: particle-image-velocimetry should show a step-like permanent displacement whose amplitude scales as 1/r and with the total volume-flux change.
  • The harmonic memory (monopole shift) may correspond to a conserved acoustic 'charge'—the time-integrated volume flux of the source—and could prove measurable as a distinct monopolar component of the displacement field.
  • Supersonic or non-barotropic flows would introduce sources for d★H, naturally leading to an acoustic analogue of null memory; extending the two-form equations to vortical flows could test whether the triangle survives beyond irrotational fluids.
  • The exact-vs-harmonic decomposition of the memory tensor suggests a gauge-invariant distinction between two physically different kinds of acoustic memory, one that can be 'gauged away' at the level of the potential and one that cannot.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper studies linear perturbations of an inviscid, irrotational, barotropic fluid. It derives an acoustic 'displacement memory': a slow change in an acoustic image source produces a lasting radial displacement of fluid particles at large distances (Sec. II, Eq. (2.22)). It then recasts the perturbation equations as a Kalb-Ramond (two-form) gauge theory, H = dB, with H closed and co-closed with respect to the acoustic metric (Sec. III, Eq. (3.13)). In the two-form language, the memory tensor Delta_AB is defined as the time integral of the leading H_uAB (Sec. V, Eq. (5.12)); its Hodge decomposition separates an exact piece, which is a large gauge transformation (Sec. VI, Eqs. (6.29)-(6.30)), from a harmonic monopole piece C epsilon_AB, which is not. The paper proposes that this establishes an 'infrared triangle' for sound and sketches a connection to scalar soft theorems using a pointlike source with a 'sonic' Lorentz factor (Sec. VII).

Significance. If the full triangle were established, this would be a notable bridge: memory, asymptotic symmetries, and soft theorems brought to a tabletop condensed-matter setting, with the Kalb-Ramond reformulation providing a clean formal tool. The paper's genuine strengths are the elementary but transparent memory derivation; the internally consistent two-form duality; and the careful Hodge-decomposition analysis distinguishing exact (symmetry) from harmonic (monopole) memory. The authors are also commendably explicit about the limitations of the soft-theorem part. However, the advertised 'first infrared triangle in a condensed matter system' is not yet supported: as detailed in the major comments, the third corner is a toy model rather than a derived acoustic statement.

major comments (2)
  1. [Sec. VII, Eq. (7.1), and Sec. VIII] The soft-theorem corner is constructed rather than derived. The point-source ansatz q(t,r)=Q sqrt(1-v^2/c^2) delta^3(r-z(t)) is introduced with the admission that it 'redefine[s] the meaning of monopole'; the match to the known scalar soft theorems requires 'a suitable choice of coupling constants', and the calculation is omitted ('We omit the detailed calculations'). Those soft theorems are statements about a relativistic scalar/two-form QFT (Refs. [39-41]), not about the Euler equations; in the acoustic problem the physical sources are image sources without a Lorentz factor (Eq. (2.5)), and there is no acoustic S-matrix. The discussion itself calls this 'a proof of principle' and 'not ... a deep statement about acoustics.' Thus the paper establishes the memory and asymptotic-symmetry corners but not a third corner within acoustics. Since the abstract and introduction claim an infrared
  2. [Sec. V, Eq. (5.13); Sec. VI, Eq. (6.30)] The memory tensor is not entirely a large gauge transformation. Eq. (5.13) decomposes Delta_AB into an exact part, 2D_[A C_B], and a harmonic part, C epsilon_AB; Eq. (6.30) states that the memory is a large gauge transformation 'except in the particular case of monopole-induced memory.' The harmonic piece is a permanent shift in the scalar monopole (Eqs. (5.22)-(5.25)) and, as the paper notes, reproduces the difficulty found by Campiglia et al. [40]. This is an honest caveat, but it is a second respect in which the 'infrared triangle' is not the standard one: monopole memory is explicitly unrelated to the asymptotic symmetries of Sec. VI. The discussion should state clearly that only the exact part of acoustic memory is tied to asymptotic symmetries, and that the harmonic part is a separate channel with no symmetry interpretation.
minor comments (5)
  1. [Sec. VII, Eq. (7.7)] The displayed formula uses a nested radical/fraction that is ambiguous; please display sqrt(c^2-v_i^2)/(c - \hat r · v_i) explicitly.
  2. [Sec. VI, after Eq. (6.10)] 'This which means' should read 'This means'.
  3. [Sec. VII, after Eq. (7.9)] 'Above, we consired' is a typo for 'Above, we considered'.
  4. [Sec. II.B, after Eq. (2.23)] 'It this does not happen' should be 'If this does not happen'.
  5. [Sec. V, opening paragraph] The asymptotic-symmetry analysis is carried out only after restricting to a homogeneous, quiescent background (rho0=c=1), while the two-form formulation of Sec. III is more general. Please state this restriction explicitly when summarizing the scope of the infrared triangle.

Circularity Check

1 steps flagged

Soft-theorem corner is constructed backwards: the source model and couplings are chosen so that the known soft-theorem kinematics reproduce the acoustic memory formula, making the third corner a fitted match rather than a derivation.

specific steps
  1. fitted input called prediction [Sec. VII, Eqs. (7.1)–(7.8); Sec. VIII]
    "we can consider a set of pointlike sources ... we pick q(t,r)= Q√(1−v^2/c^2) δ(3)(r−z(t)) ... Notice we effectively introduced a 'sonic' Lorentz factor ... In introducing a Lorentz-like factor, we are effectively redefining the meaning of 'monopole' in a way that will be convenient later on. ... with a suitable choice of coupling constants in the quantum field theory, the Braginsky–Thorne formula for the acoustic memory can be reproduced from the soft theorem. We omit the detailed calculations"

    The physical acoustic source, Eq. (2.5), is an image-source monopole with no Lorentz factor. The 'sonic' Lorentz factor in Eq. (7.1) is not derived from the Euler equations or from boundary conditions; it is inserted specifically so that the denominators in the memory formula (7.7) match the scalar soft-theorem kinematics (7.8). The matching is then completed by 'a suitable choice of coupling constants' that are free parameters, and the calculation is omitted. Thus the claimed derivation of acoustic memory from the soft theorem is a backward fit: the source model and couplings are chosen to reproduce the already-known memory formula, so the soft-theorem corner reduces by construction to its input. The paper itself confirms this in Sec. VIII: it is 'a proof of principle' where one can 'cons

full rationale

The memory corner (Sec. II and Sec. V) and the asymptotic-symmetry corner (Sec. VI) are derived within the acoustic system: the wave-equation memory follows from the retarded Green function, and the exact/harmonic decomposition of the two-form memory tensor is a mathematical Hodge decomposition with the exact piece identified with large gauge transformations. No load-bearing self-citation or imported uniqueness theorem is involved. The circularity is confined to the third corner, Sec. VII, where the soft-theorem connection is not derived for Euler acoustics: the source is given a relativistic 'sonic' Lorentz factor ad hoc, the coupling constants are left free, and the detailed calculation is omitted. Since the abstract's central claim is 'the first example of an infrared triangle in a condensed matter system,' and that triangle explicitly includes the soft-theorem corner, the fitted construction is load-bearing. I therefore assign 6: two corners are independent and substantive, but the third corner reduces to a fit by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 3 invented entities

The central claim rests on standard fluid assumptions (inviscid, irrotational, barotropic; linear perturbations), topological facts about R^2×S^2, specified falloffs at infinity, and prior scalar two-form asymptotic symmetry results. The only truly ad hoc inputs are the image-source model and the 'sonic' Lorentz factor used to connect to soft theorems.

free parameters (3)
  • Q(t) source monopole = arbitrary prescribed function (e.g., d/dt[4π a(t)^3/3])
    The memory magnitude is proportional to ΔQ; the effect's existence is derived, but its size is an input from the chosen source model (Sec. II).
  • Sonic Lorentz factor √(1-v^2/c^2) in Eq. (7.1) = 1 at v=0; renormalizes Q by velocity
    Introduced ad hoc so the point-source solution matches the denominators of known soft theorems; the paper admits this redefines the monopole (Sec. VII).
  • Coupling constants in scalar QFT soft-theorem comparison = Unspecified ('suitable choice')
    Required to make the soft theorem reproduce Eq. (7.7); no derivation is given (Sec. VII).
axioms (7)
  • domain assumption Fluid is inviscid, irrotational, barotropic; perturbations are adiabatic; vorticity initially zero
    Needed for v=∇φ and for d★H=0; enters Eqs. (2.10)-(2.13) and (3.9)-(3.12).
  • domain assumption Background homogeneous, quiescent, Φ=0 for the memory derivation and for Sections V-VII
    Used to reduce the acoustic metric to Minkowski and to get the simple wave equation; Sec. IIA and Sec. V.
  • standard math Radiation zone topology is R^2×S^2; closed forms are exact up to the sphere's harmonic two-form
    Justifies global introduction of B; uses de Rham cohomology and Künneth formula (Sec. IIIA, Appendix A).
  • domain assumption Large-r falloffs (5.5), (5.15), (5.16), including logarithmic terms, hold
    Boundary conditions for finite-energy radiation; taken from Refs. [8,41,57,58]; load-bearing for the asymptotic symmetry analysis.
  • domain assumption Prior results: scalars have asymptotic symmetries via a dual two-form (Campiglia et al., Francia and Heissenberg, Heissenberg)
    The acoustic asymptotic symmetry analysis inherits these theorems (Secs. I, VI, VII).
  • standard math Lorenz gauge is reachable for B and A with reducible gauge-for-gauge freedoms
    Standard p-form gauge theory; used to derive the wave equations in Secs. IIIA and VI.
  • ad hoc to paper Image-source q in the continuity equation reproduces the moving-boundary problem outside the source region
    The source is introduced as a trick and the interior is treated as unphysical; all acoustic memory magnitudes depend on this modeling (Sec. IIA).
invented entities (3)
  • Image sources (fictitious volume sources q) no independent evidence
    purpose: Replace moving boundary conditions by a source in the continuity equation
    Explicitly unphysical; introduced in Sec. IIA and used throughout.
  • Kalb-Ramond two-form potential B for sound no independent evidence
    purpose: Reformulate linear acoustics as a gauge theory to access asymptotic symmetries
    Derived gauge potential for H in the radiation zone; a mathematical dual description, not a new physical field with independent evidence.
  • Pointlike acoustic sources with a 'sonic' Lorentz factor (Eq. (7.1)) no independent evidence
    purpose: Make the retarded solution match the kinematic denominators of known soft theorems
    Ad hoc redefinition of source monopole; admitted in Sec. VII.

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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.

Figures

Figures reproduced from arXiv: 2512.15796 by Andr\'e G. S. Landulfo, N\'ickolas de Aguiar Alves.

Figure 1
Figure 1. Figure 1: FIG. 1. Left: a moving surface, such as a sphere with oscillating radius, disturbs the fluid around it and generated sound waves. Right: using the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

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