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arxiv: 2605.19356 · v1 · pith:HLIYB4WGnew · submitted 2026-05-19 · ✦ hep-th

Perfect fluid equations with nonrelativistic conformal supersymmetries

Timofei Snegirev This is my paper

Pith reviewed 2026-05-20 04:48 UTC · model grok-4.3

classification ✦ hep-th
keywords perfect fluidsnonrelativistic supersymmetryconformal Newton-Hooke algebral-conformal Galilei superalgebraHamiltonian formalismconserved chargesanticommuting fieldsLagrangian description
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The pith

Perfect fluid equations admit extensions with N=2 conformal Newton-Hooke and N=1 l-conformal Galilei supersymmetry via anticommuting superpartner fields.

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

The paper extends earlier constructions of supersymmetric perfect fluids to two additional nonrelativistic conformal supersymmetries. It introduces real or complex anticommuting fields as superpartners to the fluid density and velocity inside a Hamiltonian framework. For both the N=2 conformal Newton-Hooke superalgebra and the N=1 l-conformal Galilei superalgebra with arbitrary half-integer l, the authors construct the complete set of conserved charges and supply the corresponding Lagrangian descriptions. This shows that the fluid equations can carry these larger symmetry structures without breaking their original form. A reader would care because the result enlarges the family of known supersymmetric fluid models and indicates how nonrelativistic conformal symmetry can be realized in hydrodynamic settings.

Core claim

Perfect fluid equations can be equipped with the N=2 conformal Newton-Hooke superalgebra and the N=1 l-conformal Galilei superalgebra (for arbitrary half-integer l) by introducing appropriate anticommuting superpartner fields in the Hamiltonian framework, constructing all associated conserved charges, and deriving the corresponding Lagrangians, although subtleties appear when attempting the N=2 l-conformal Galilei case.

What carries the argument

The central mechanism is the introduction of real (for N=1) or complex (for N=2) anticommuting field variables as superpartners for the density and velocity; these fields generate the supersymmetry transformations while the full set of Noether charges reproduces the target superalgebra.

If this is right

  • The full superalgebra is realized on the fluid variables through the constructed charges.
  • Lagrangian formulations exist that reproduce the Hamiltonian dynamics for each case.
  • The construction applies for any half-integer value of the parameter l in the Galilei superalgebra.
  • The same Hamiltonian method yields both the N=2 Newton-Hooke and N=1 Galilei supersymmetric fluids.

Where Pith is reading between the lines

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

  • These models could supply concrete examples of supersymmetric hydrodynamics in systems that exhibit nonrelativistic conformal invariance, such as certain cold-atom or condensed-matter setups.
  • One could examine the limit in which the superpartners are integrated out or set to zero to recover ordinary perfect-fluid behavior and check for consistency.
  • Similar constructions might be attempted for other nonrelativistic superalgebras that lie outside the two cases treated here.

Load-bearing premise

Anticommuting superpartner fields can be consistently coupled to the perfect fluid variables while preserving both the fluid equations and the full superalgebra structure without additional constraints or inconsistencies.

What would settle it

Compute the Poisson brackets among the constructed conserved charges and check whether they close exactly into the claimed N=2 conformal Newton-Hooke or N=1 l-conformal Galilei superalgebra; or vary the given Lagrangian and verify that the resulting equations of motion recover the original perfect fluid dynamics plus the superpartner sector.

read the original abstract

Our recent result on the construction of perfect fluid equations with N=1,2 Schr\"odinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases are considered in detail, which include the N=2 conformal Newton-Hooke superalgebra and N=1 l-conformal Galilei superalgebra with arbitrary half-integer parameter l. Supersymmetric fluid models are built within the Hamiltonian framework by introducing real (for N=1) or complex (for N=2) anticommuting field variables as superpartners for the density and velocity. For both the cases the full set of conserved charges associated with the superalgebras is constructed and the Lagrangian description is given. Subtleties with the construction of perfect fluid equations with N=2 l-conformal Galilei supersymmetry are discussed as well.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript extends the authors' prior construction of perfect fluid equations with N=1,2 Schrödinger supersymmetry to nonrelativistic conformal supersymmetries. It treats in detail the N=2 conformal Newton-Hooke superalgebra and the N=1 l-conformal Galilei superalgebra (arbitrary half-integer l). Supersymmetric models are built in the Hamiltonian framework by introducing real (N=1) or complex (N=2) anticommuting superpartner fields for the density and velocity; the full set of conserved charges is constructed and a Lagrangian description is supplied. Subtleties for the N=2 l-conformal Galilei case are noted but the case is set aside.

Significance. If the constructions are internally consistent, the work supplies explicit, algebra-preserving supersymmetric extensions of perfect-fluid dynamics for two additional nonrelativistic superalgebras. The explicit construction of the complete charge set and the Lagrangian, together with the treatment of arbitrary l, constitutes a concrete technical advance that can serve as a starting point for further studies of supersymmetric hydrodynamics in nonrelativistic settings.

minor comments (3)
  1. The abstract states that subtleties arise for N=2 l-conformal Galilei supersymmetry; a concise paragraph in the main text (perhaps near the end of the introduction or in a dedicated subsection) explaining the precise obstruction would help readers understand why the case is deferred.
  2. Notation for the superpartner fields (real vs. complex) and their Poisson brackets with the fluid variables should be introduced once, early in the Hamiltonian section, to avoid repeated re-definition later.
  3. The connection to the cited prior result (Mod. Phys. Lett. A 41 (2026) 2550214) is mentioned but the precise differences in the superalgebra generators and in the fluid variables between the two papers could be summarized in a short table or bullet list.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and for recommending minor revision. The report confirms the internal consistency of the constructions for the N=2 conformal Newton-Hooke and N=1 l-conformal Galilei cases, along with the explicit charge algebra and Lagrangian descriptions. We have no major objections to address and will incorporate any minor editorial suggestions in the revised version.

Circularity Check

0 steps flagged

No significant circularity; explicit construction is self-contained

full rationale

The paper extends a prior result by the same author on Schrödinger supersymmetry to the N=2 conformal Newton-Hooke and N=1 l-conformal Galilei cases through direct introduction of real or complex anticommuting superpartner fields for density and velocity in the Hamiltonian framework, followed by explicit construction of the full set of conserved charges and the Lagrangian. No step reduces the new charges, equations, or algebra closure to a fit, definition, or ansatz taken from the cited prior work; the extension is presented as an independent verification by construction that the superalgebra is preserved on the fluid dynamics. The self-citation functions only as background context rather than a load-bearing premise, and the paper notes subtleties for the excluded N=2 l-Galilei case without forcing the treated cases to inherit results by definition.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The constructions rest on the existence and consistency of the cited superalgebras plus the assumption that anticommuting fields can be introduced as superpartners without violating fluid continuity or momentum equations.

axioms (2)
  • domain assumption The N=2 conformal Newton-Hooke superalgebra and N=1 l-conformal Galilei superalgebra with half-integer l close under the required (anti)commutators.
    Invoked when constructing the conserved charges associated with the superalgebras.
  • ad hoc to paper Anticommuting fields can be coupled to density and velocity while preserving the perfect-fluid continuity and Euler equations.
    Central modeling choice stated in the abstract for the Hamiltonian framework.
invented entities (1)
  • Real or complex anticommuting superpartner fields for density and velocity no independent evidence
    purpose: To realize the supersymmetry transformations within the fluid variables
    Introduced explicitly in the abstract as the key new ingredient for both cases.

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Reference graph

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