{"id":"5f5089c0-8ca4-42ab-ac09-3fdc16a29f24","arxiv_id":"2512.23793","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"For Gaussian initial states, vortex modes contribute a finite, non-local stress response in a quantum perfect fluid, calculable without adding symmetry-breaking regulators.","lead":"Quantum perfect fluids with zero-energy vortex modes can still have well-defined dynamical correlations if the experiment starts in a broad Gaussian quantum state. This makes quantum vortex contributions to the fluid's stress response calculable without breaking the symmetry that defines the fluid.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Higher-loop τ-cancellation is the load-bearing assumption: the one-loop response is safe, but the advertised perturbative calculability of generic correlators remains unproven unless the Section IV τ-dependence cancels.","rationale":"I read the paper as making two claims of different strength: (i) a concrete one-loop calculation of the retarded stress-tensor response, and (ii) a broader assertion that correlators in the Gaussian initial states are generally well-defined and calculable in perturbation theory. Claim (i) is self-contained: the Feynman rules are explicit, the master integrals are reduced by Mellin-Barnes and method of regions, and the one-loop diagrams contain no internal vertices, so they are insensitive to the arbitrary final-time slice τ. I found no internal inconsistency in the one-loop response itself. Claim (ii), however, is not established by the computation presented. The paper's own Section IV flags the unresolved τ-dependence of higher-loop diagrams. That is the single most load-bearing assumption: if τ does not cancel, the perturbative framework is not a unitary quantum-mechanical expansion and the abstract's promise of accessible correlators fails beyond the one-loop channel. The reader identified exactly this point as the weakest assumption, and I agree. The unresolved τ-cancellation, combined with the uncomputed special-Δ behavior and the state-dependence of the result, justifies the CONDITIONAL verdict rather than an outright ACCEPT. I would not move the verdict further because the one-loop result is a genuine, explicitly calculated contribution and the paper is honest about the limitation.","tokens_in":27963,"tokens_out":13512,"duration_ms":142013,"concrete_test":"Compute the leading τ-sensitive correction: for example, the contribution to ⟨T^{0i}T^{0j}⟩ at one loop with one cubic vertex (or the T-mode self-energy at two loops) obtained from the expansion of Eq. (3), keeping the final-time boundary τ of Eq. (2) explicit in all time integrals over [0, τ]. Sum all plus/minus branch diagrams at that order and isolate the coefficient of τ. If the τ-dependent terms cancel, the unitarity assumption is supported and the central claim survives; if a residual ∼ μ ĉ_T τ term remains, the perturbative expansion is not well-defined beyond the leading one-loop response.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's broad abstract claim—that correlators in these Gaussian initial states are well-defined and accessible in perturbation theory—is actually demonstrated only for a single one-loop channel, where no interaction vertex lies on the contour segment [0, τ]. The decisive assumption is explicitly identified in Section IV: at higher orders, diagrams with interaction vertices connected to external T-mode propagators integrate over intermediate times using the free Wightman function (20), which grows with time; such integrals can produce terms proportional to μ ĉ_T τ. Unitarity of the interacting EFT would force these terms to cancel between the plus and minus branches of the Schwinger-Keldysh contour, but the paper states: 'It will require an explicit calculation to determine which of these two alternatives is actually realized.' If the τ-dependence survives, generic correlators—e.g., ⟨T^{0i}T^{0j}⟩ or any observable with external T legs—acquire IR power divergences controlled by μ ĉ_T τ, and the advertised calculability breaks down beyond the one-loop response computed here. This is not a flaw in the one-loop result, but it is exactly where the strongest claim is least secure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Schwinger-Keldysh (in-in) framework for the EFT of zero-temperature perfect fluids in which the infinite degeneracy of the ω_T=0 vortex modes is regulated not by deforming the SDiff-invariant Lagrangian but by preparing the system in a normalizable Gaussian initial state at t=0. The state width acts as an infrared regulator, making the free vortex Wightman function (20) non-degenerate at finite times. The authors compute the leading one-loop retarded stress-tensor response in d=3 (Eqs. (26)-(27)), splitting it into a mixed phonon-vortex term G_R^{TL}, a two-phonon term G_R^{LL}, and a pure TT term that is time-independent and therefore drops out of the retarded commutator. The advertised result is that vortex modes give an IR-finite, non-local contribution parametrized by the state data (μ, ĉ_T, Δ) without explicit SDiff breaking. The paper also argues (Appendix A) that prior IR-safe claims based on dimensional regularization are regulator-dependent.","tokens_in":28243,"tokens_out":18134,"duration_ms":177066,"significance":"Provided the one-loop calculation is correct, this is a significant step: it gives the first calculable, IR-finite stress-tensor response involving the vortex sector of the perfect-fluid EFT without adding c_T-breaking terms, and it casts the vortex IR problem in state-dependent language consistent with the free-particle analogy for the zero-energy modes. The calculation is explicit and self-contained, with master integrals in Appendix B and the known superfluid (phonon) response recovered in the LL channel as a cross-check. The state parameters are genuine inputs, so there is no circularity of fitting output to input. The paper is unusually candid about its own limitation: Section IV explicitly leaves open the τ-independence of higher-loop diagrams. That limitation is exactly the boundary of the strongest claim in the abstract, so the breadth of the claim exceeds the demonstrated result. The Appendix A critique of ref. [8] is a substantive referee-relevant contribution but should itself be scrutinized.","major_comments":[{"comment":"The abstract claims that correlators in these Gaussian states are 'well-defined and accessible via perturbation theory,' but the advertised scope is not established beyond the one-loop channel computed here. As the last paragraph of Section IV states, diagrams with interaction vertices on the contour segment [0,τ] of Eq. (2) integrate the free vortex Wightman function (20), which grows linearly in time, and may produce terms proportional to μĉ_Tτ. The paper explicitly writes: 'It will require an explicit calculation to determine which of these two alternatives is actually realized.' The computed G_R is safe because no vertex lies in this segment, but for generic observables such as ⟨T^{0i}T^{0j}⟩ the τ-dependence is the crux. Please either provide a minimal explicit check (e.g., a two-loop diagram with a T-line vertex) or reformulate the abstract and conclusions to claim only the one-loo","section":"Abstract and Section IV"},{"comment":"The prefactor of G_R^{TL} contains 1/sin(πΔ/2) and 1/Δ, giving poles at all even integer Δ (a double pole at Δ=0). These values satisfy the admissibility condition Δ>-d of Eq. (16) and include the natural scale-invariant kernel Δ=0, so they are legitimate physical states, not artificial regulator poles. The statement that the integrals are IR/UV finite 'for generic values of the spectral index Δ' leaves the behavior at these isolated values open. Please explain whether these poles reflect logarithmic IR divergences that require an additional Δ-regularization, and specify the domain of Δ (possibly excluding even integers) on which Eq. (26) is the physical response.","section":"Section III, Eq. (26)"}],"minor_comments":[{"comment":"In the LL ('superfluid') term the second projector is written P_T^{jl}; for the two-phonon channel it should presumably be P_L^{jl}. As printed it conflicts with the caption of Fig. 1(c) and with the text describing two L-phonon intermediate states.","section":"Eq. (24)"},{"comment":"The vertical and horizontal axes are unlabeled. Please label them (likely G_R^{TL} scaled by t^5 and c_s t|p|) and state the Δ values for each curve so the plot is readable.","section":"Fig. 2"},{"comment":"Notation for the functions g_R is inconsistent: Eq. (26) uses g^{TL}_R while Eq. (27) introduces g^{R,LL}. Unify, and define the argument z=c_s t|p| once.","section":"Eqs. (26)-(27)"},{"comment":"The shorthand 'perms' is used without specifying the symmetrization of the external indices; for reproducibility, state the sum over index permutations and any symmetry factors.","section":"Eqs. (22)-(24)"},{"comment":"The Mellin-Barnes contour contraction and the analyticity domain of (B2) for z=-ic_s t+0^+ could be stated more explicitly; as written it is terse for a central technical input.","section":"Appendix B"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The one-loop calculation appears sound and the paper is a genuine contribution, but I do not think the abstract's broad claim is supported by the evidence in the manuscript; the Section IV caveat is exactly the load-bearing point. I would ask the authors to add at least one explicit higher-loop check of τ-independence (or suitably narrow the claims) and to clarify the even-Δ poles of Eq. (26). The Appendix A critique of ref. [8] is stated with considerable confidence and carries some weight for the literature; a second referee familiar with the subtleties of dimensional regularization should scrutinize that comparison."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper's one-loop result is real and worth engaging. The core move — using a Gaussian initial-state width as an IR regulator while keeping the classical action SDiff-invariant — is new relative to the c_T-deformation and algebraic vorton approaches. And the explicit d=3 retarded stress-tensor response, Eqs. (26)–(27), is a concrete, nontrivial result: the TT loop is time-independent and drops out, the TL mixed term is nonlocal and finite for generic Δ, and the LL term reproduces the standard superfluid response. That is a working example of what the authors promise: vortex-sector observables without breaking SDiff in the Lagrangian.\n\nThe calculation looks honest and internally coherent. The master integrals are in Appendix B, and the authors are unusually clear about what they have not shown. Section IV explicitly states that higher-loop diagrams with external T legs may develop τ-dependence, and that an explicit calculation is needed to see whether unitarity cancels it. That is the right statement, and it is the main soft spot: the abstract's claim that correlators are well-defined and accessible in perturbation theory is demonstrated here for only one channel at one loop. If the τ-dependence survives, the advertised calculability breaks down beyond this result. The reader's stress-test is accurate, and the authors already concede it.\n\nTwo smaller issues. Eq. (26) has poles at special values of Δ (the sin(πΔ/2) denominator), and the physical status of those points is not discussed. And the appendix A critique of Gripaios-Sutherland, while plausible, rests on a regulator-comparison calculation that is described but not fully displayed; a referee should push on that. The free parameters μ, ĉ_T, Δ are state-preparation inputs, not extracted from the output — that is fine and by design, not circular.\n\nBottom line: this is a method paper with one solid, explicit result and an unfinished program. The one-loop calculation deserves a serious referee, and the paper would be a good contribution if the τ-cancellation is either proven or its failure bounded. I'd bring it to the group with the caveat that it is genuinely preliminary beyond one loop.","headline":"A genuinely new method for defining vortex-sector correlators in perfect-fluid EFT, but the advertised programmatic claim rests on an explicitly unproven higher-loop cancellation.","tokens_in":28712,"tokens_out":1839,"would_cite":true,"duration_ms":17281,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81T18","81T15"],"pacs":["11.10.-z","67.10.-j"],"model":"deepseek-v4-flash","headline":"This paper shows that the retarded stress-tensor response of a quantum perfect fluid is finite and nonlocal in space and time when the fluid is prepared in a semiclassical Gaussian state at t=0, with vortex modes contributing a well-defined","keywords":["perfect fluid","effective field theory","quantum hydrodynamics","vortex modes","SDiff invariance","Schwinger-Keldysh","initial state","stress tensor response"],"falsifier":"Calculate the one-loop (or higher-loop) contribution to an observable that connects interaction vertices to external vortex-line propagators—for instance the energy-flux correlator ⟨T^{0i}T^{0j}⟩—and check whether the dependence on the final time slice τ cancels after summing all diagrams. The paper states that an explicit calculation is needed to determine which alternative is realized; if τ-dependence survives, the Gaussian-state prescription does not yield well-defined generic correlators.","tokens_in":27819,"feed_emoji":"🌀","tokens_out":5708,"duration_ms":47899,"temperature":0.7,"pith_summary":"The paper confronts a long-standing obstacle in quantizing perfect fluids: the exact volume-preserving-diffeomorphism (SDiff) symmetry forces vortex (transverse) modes to have zero dispersion, so the theory has no normalizable vacuum and ordinary perturbative correlators are ill-defined. The authors' proposal is to stop asking for vacuum correlators and instead compute expectation values in a semi-classical Gaussian initial state prepared at t=0; the width of this state acts as an infrared regulator without touching the SDiff-invariant Lagrangian. Using the Schwinger-Keldysh formalism, they compute the retarded stress-tensor two-point function in d=3 and find that the vortex modes produce a well-defined, non-local-in-space-and-time term, added to the usual superfluid (phonon) response. If correct, this gives a practical route to vortex-sector observables in the perfect-fluid EFT without adding symmetry-breaking regulators, and it predicts a specific departure from superfluid response at finite compressibility. The paper is careful that the full perturbative programme still depends on a cancellation of the arbitrary final-time slice τ; this is the main caveat.","feed_headline":"Vortex modes give finite, nonlocal response in quantum fluids","feed_subtitle":"A Gaussian state at t=0 regulates the zero-energy vortex modes without breaking the fluid's symmetries, at least at short times.","key_machinery":"The central technical object is the Gaussian initial-state wavefunctional Ψ_i[φ]=N exp(-½∫π^I K_IJ π^J + i∫v·π), whose kernel K_ij(p)=P_L K_L(p)+P_T K_T(p) fixes the t=0 velocity and density fluctuations; for the transverse (vortex) part they take a power law K_T(p)=w0 ĉ_T μ(|p|/μ)^Δ. Inserted into the Schwinger-Keldysh path integral, this kernel turns the free vortex propagator into W^T_p(x0,y0) = (1 - i x0 K_T/w0)(1 + i y0 K_T/w0)/(2K_T), which is non-degenerate at finite times and grows linearly in time, mirroring the spreading of a free-particle wavepacket. Through the time-momentum Feynman rules, all one-loop tensor integrals reduce to master integrals I_{αβ}(p,z) of the form ∫_k e^{-z","core_discovery":"In the Schwinger-Keldysh (in-in) representation, the authors choose an initial Gaussian wavefunctional centered on the static, homogeneous fluid configuration, with a transverse kernel K_T(p)=w0 ĉ_T μ (|p|/μ)^Δ. This makes the vortex Wightman propagator non-degenerate in time—W_T grows linearly with the observation times—so loop integrals are infrared finite for generic spectral index Δ, with no need for the c_T deformation of the classical action. Evaluating the one-loop retarded stress-tensor response in d=3, they obtain G_R(p,t)=G_R^{TL}(p,t)+G_R^{LL}(p,t), where the mixed phonon–vortex term (Eq. (26)) is finite for generic Δ and vanishes in the incompressible limit c_s→∞, and the pure v","pith_inferences":["If the τ-cancellation is confirmed, the Gaussian-state construction effectively defines a family of physical 'quantum fluid' states that interpolate continuously between stable superfluid-like behaviour and strongly vortex-dominated behaviour as Δ and ĉ_T vary; this could be used to model far-from-equilibrium vortex dynamics.","The scheme suggests a testable criterion: in this approach, IR safety is not a property of SDiff-invariant operators alone (as a gauge-symmetry picture would suggest), but of the combination of state and operator; the appendix's regulator comparison indicates the two pictures are genuinely inequivalent.","One could extend the same initial-state technique to compute out-of-time-order correlators or energy fluxes, where the linear-in-time growth of vortex Wightman functions might produce measurable time growth; the τ-cancellation check for ⟨T^{0i}T^{0j}⟩ is the natural next calculation.","For d=2, the kernel admits parity-violating and L–T mixing terms (Eq. (13)) that would generate vorticity and chirality in the response; the parity-conserving computation here is a special case that could be extended."],"forward_implications":["The retarded stress-tensor response of a quantum perfect fluid is finite and calculable without adding any SDiff-breaking terms to the Lagrangian, as long as one works in a Gaussian initial state and at short times.","The pure vortex (TT) loop is time-independent at one loop, so it drops out of the causal response; the leading vortex signature appears through the mixed phonon–vortex (TL) term.","The vortex contribution vanishes as c_s→∞ (incompressible limit) but is present at finite compressibility, giving a concrete, parameter-dependent deviation from superfluid response.","Correlators of generic local operators, and even energy-flux correlators where external T-mode propagators appear, should be accessible in the same way, provided the final-time-slice dependence cancels by perturbative unitarity.","The results depend only on the initial-state parameters (w0, c_s, μ, Δ, ĉ_T) which are in principle measurable at t=0."],"fun_headline_variants":["Quantum fluid vortices regulated by Gaussian states","Finite vortex response in quantum perfect fluids","Taming zero-frequency vortices in quantum fluids","Nonlocal vortex response via Gaussian initial states"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole calculation assumes that the interacting quantum theory remains unitary over short times, so that the arbitrary final-time slice τ drops out of physical results; if that fails, the method stops producing well-defined answers for generic correlators.","fun_headline_variants_meta":{"raw":{"variants":["Quantum fluid vortices regulated by Gaussian states","Finite vortex response in quantum perfect fluids","Taming zero-frequency vortices in quantum fluids","Nonlocal vortex response via Gaussian initial states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00013,"raw_usage":{"total_tokens":961,"prompt_tokens":739,"completion_tokens":222,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":483,"completion_tokens_details":{"reasoning_tokens":166}},"tokens_in":483,"tokens_out":222,"duration_ms":2410,"temperature":1.0,"reasoning_tokens":166,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T13:35:22.743326+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Calculate the one-loop (or higher-loop) contribution to an observable that connects interaction vertices to external vortex-line propagators—for instance the energy-flux correlator ⟨T^{0i}T^{0j}⟩—and check whether the dependence on the final time slice τ cancels after summing all diagrams. The paper states that an explicit calculation is needed to determine which alternative is realized; if τ-dependence survives, the Gaussian-state prescription does not yield well-defined generic correlators.","supporting_citations":[],"review_version":1}