{"id":"e115eef2-80d7-493b-8618-ac67e8f74978","arxiv_id":"2505.05448","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For a massless conformally coupled scalar field in rigidly rotating thermal states on AdS3 and AdS4, relativistic kinetic theory approximates the quantum stress-energy tensor well at high temperatures, and the quantum heat flux always opposes the rotation.","lead":"This paper computes the quantum stress-energy tensor of a massless scalar field in a rotating hot state on anti-de Sitter spacetime, and compares it with a classical gas approximation. The classical approximation works well at high temperature, while quantum effects produce a heat flow opposite to the rotation direction.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified; the cited rotating-vacuum identity is the least secure premise but is well supported.","rationale":"I agree with the reader that the rotating-vacuum identity is the weakest assumption in the argument. But because that identity is well supported by the cited prior work and is physically expected for a conformal scalar with no speed-of-light surface, it does not undermine the central claim. The 4D results depend on a supplementary notebook, and an earlier version of that notebook contained an acknowledged error; this is a reproducibility limitation rather than a demonstrated flaw, and the corrected notebook plus the fully displayed 3D formulas provide independent support. A targeted verification of the vacuum identity would still be a worthwhile check, but the paper's conclusion is not overturned.","tokens_in":11563,"tokens_out":23343,"duration_ms":279006,"concrete_test":"Independently construct the vacuum two-point function in rotating coordinates by summing Dirichlet mode functions with positive frequency with respect to the co-rotating Killing vector for representative Ω (e.g., 0, 0.5, 0.96) and compare with Eqs. (4.4)-(4.6). If the two-point functions agree identically, the subtraction (4.3) is fully justified; if not, the QFT-RSET, the RKT comparison, and the heat-flux conclusion would need re-evaluation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central comparison in Sec. 4 subtracts the non-rotating vacuum RSET (4.2) from the rigidly-rotating thermal RSET, relying on the assertion that the rotating vacuum is the same as the non-rotating AdS vacuum [15,16]. If this identity failed for the Dirichlet boundary conditions used, the QFT-RSET (4.15), the comparison with RKT, and the sign of the heat flux would all change. This is the least secure premise because it is cited rather than re-derived. However, it is not a fatal flaw: for the conformally coupled massless scalar with |Ω|<1, the co-rotating Killing vector is timelike everywhere and the AdS mode spectrum keeps all co-rotating frequencies positive, which is precisely the content of [15,16]. No internal inconsistency was found in the image-sum construction, the high-temperature limit, or the claimed signs of the heat flux and anisotropic stress.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a massless, conformally coupled scalar field in rigidly rotating thermal states on three- and four-dimensional anti-de Sitter spacetime, assuming |Ω|<1 so that no speed-of-light surface is present. It first derives the stress-energy tensor from relativistic kinetic theory (RKT), modelling the field as a thermal gas of massless bosons, and then computes the difference between the renormalized stress-energy tensors of the rigidly rotating thermal state and the vacuum state using a Matsubara/image-sum construction. The two stress-energy tensors are compared through the thermometer-frame decomposition. The central findings are that RKT approximates the QFT stress-energy tensor very well at high temperatures for all angular speeds considered, that the energy density has a maximum at the origin and decreases monotonically toward the AdS boundary, that the azimuthal heat flux is always negative (so the quantum radiation rotates more slowly than the rigid frame), and that in four dimensions the scalar stress-energy tensor has an additional anisotropic-stress component compared with the fermionic case.","tokens_in":11703,"tokens_out":20375,"duration_ms":213472,"significance":"If the results hold, the paper provides the first systematic comparison between kinetic-theory and full QFT stress-energy tensors for rotating bosonic thermal states on AdS, extending earlier work on non-rotating scalars and rotating fermions. The comparison is parameter-free: the RKT calculation contains no fitted quantities and the QFT result is derived from standard Hadamard and Matsubara machinery, with the three-dimensional formulas written out in full. The paper also makes falsifiable predictions about the sign of the heat flux and the angular structure of the anisotropic stress, and it makes the numerical data and a supplementary Mathematica notebook publicly available. The least secure premise, the identification of the rigidly-rotating vacuum with the non-rotating AdS vacuum, is cited from earlier work and is physically well motivated for |Ω|<1, so the overall argument is credible.","major_comments":[],"minor_comments":[{"comment":"The assertion that the rigidly-rotating vacuum state is identical to the non-rotating AdS vacuum is cited from [15,16] and not re-derived; since the thermal subtraction (4.3) and the comparison in Sec. 5 rely on this identity, the authors should add a brief justification or a precise statement of the conditions under which it holds for the Dirichlet boundary conditions used in this paper.","section":"Sec. 4, Eq. (4.3)"},{"comment":"The four-dimensional expressions for the QFT-RSET are not displayed in the main text and are relegated to the supplementary Mathematica notebook [21]; because the four-dimensional comparison is a central result, the authors should ensure the notebook is self-contained and permanently archived, and should state explicitly how the notebook expressions map onto the frame components (4.15).","section":"Sec. 4, after Eq. (4.14)"},{"comment":"The statement that the energy density 'always' has a maximum at the origin is stronger than the numerical evidence, which covers a discrete set of β and Ω values; I suggest qualifying the claim to the parameter ranges studied or providing an analytic argument.","section":"Sec. 6, first paragraph"},{"comment":"The notation X_{j,0} for the sum over all nonzero integers j is nonstandard and could be misread as a double index; writing ∑_{j≠0} explicitly would be clearer.","section":"Eq. (4.11)"},{"comment":"The quantitative support for 'excellent approximation' would be strengthened if the text quoted the maximum relative difference between the RKT and QFT energy densities for the displayed parameter values, since at present the claim is supported only visually.","section":"Sec. 5, Figs. 2, 3, and 6"}],"recommendation":"accept","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nWhat you should know first: this is a clean, well-scoped calculation of the renormalized stress-energy tensor for a massless conformally coupled scalar in rigidly rotating thermal states on AdS3 and AdS4, with a side-by-side comparison against relativistic kinetic theory. The headline claims hold up: at high temperature, RKT is an excellent approximation even close to the maximum angular speed; at low temperature, quantum effects are substantial. The heat flux is negative (the radiation lags the rotation) and the scalar SET has an extra anisotropic-stress component absent in the fermionic case. The paper delivers what it promises.\n\nWhat is actually new: this is the first rotating thermal scalar RSET on AdS; prior work covered rotating fermions [9,10] and nonrotating scalars [4]. The methods are standard extensions of those papers, but the application and the qualitative scalar-vs-fermion contrast are new. The RKT computation is independent, and the high-temperature agreement is a good check, not a circular comparison.\n\nThe soft spots are real but minor. The 4D RSET formulas are relegated to a supplementary Mathematica notebook; combined with the acknowledged error in an earlier version of that notebook, this makes verification harder. This is not fatal, but the supplementary material needs to be complete and clearly versioned. The weakest premise is the rotating-vacuum identity, cited from [15,16] without re-derivation. If that identity fails for the Dirichlet boundary conditions used, the subtraction in (4.3) and hence the whole QFT-RSET would shift. I think the identity is correct for |Ω|<1—the co-rotating Killing vector is timelike everywhere and the mode frequencies stay positive—but a referee should confirm the cited proof actually covers the Dirichlet case.\n\nThe paper is honest about what it does and does not do: it compares differences of expectation values, notes the anomalous trace separately, and leaves backreaction to future work. The plots support the claims. No internal inconsistencies jump out.\n\nBottom line: this is a solid letter for the QFT-in-curved-spacetime audience. It deserves a serious referee and, after the supplementary notebook is checked, acceptance. I would cite it if I were working on RSETs in AdS or on rotating thermal states. It is not field-changing, but it fills a genuine gap and the fermion comparison is worth knowing.","headline":"Clean, well-scoped first computation of the rotating thermal scalar RSET on AdS3/AdS4; high-temperature RKT agreement holds, and the main caveats are the cited rotating-vacuum identity and reliance on a supplementary notebook.","tokens_in":12251,"tokens_out":3158,"would_cite":true,"duration_ms":30981,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For a conformally coupled scalar field in rigidly rotating thermal states on three- and four-dimensional AdS, relativistic kinetic theory matches QFT at high temperature while quantum effects dominate at low temperature.","keywords":["anti-de Sitter spacetime","rigidly rotating thermal states","renormalized stress-energy tensor","quantum scalar field","relativistic kinetic theory","heat flux","conformal coupling","imaginary-time sum"],"falsifier":"Directly compute the rigidly-rotating vacuum two-point function for the Dirichlet scalar field and compare it with the non-rotating AdS vacuum Green function; any nonzero difference at order $\\Omega^2$ would alter the subtracted stress-energy tensor and would appear as a change in the predicted heat flux.","tokens_in":11348,"feed_emoji":"🌀","tokens_out":13147,"duration_ms":113257,"temperature":0.7,"pith_summary":"This paper asks what happens to the energy, pressure, and flow of a quantum field when a thermal bath on anti-de Sitter spacetime is made to rotate rigidly. For a massless, conformally coupled scalar field in three and four spacetime dimensions, it computes the renormalized stress-energy tensor from quantum field theory and compares it with relativistic kinetic theory, which treats the field as a classical gas of massless particles. The central claim is that the classical-gas approximation is very accurate at high temperature for every allowed rotation speed, while at low temperature quantum corrections are large. The paper also reports that the energy density always peaks at the centre and falls monotonically to the boundary, that the azimuthal heat flux is always negative, meaning the quantum radiation rotates more slowly than the rigid frame, and that the scalar field's stress tensor has more independent anisotropic-stress components than the corresponding fermion field.","feed_headline":"Quantum heat flux lags a rotating AdS bath","feed_subtitle":"At high temperature the bath matches classical kinetic theory, but the heat current points opposite to rotation.","key_machinery":"The central object is the difference Green function $\\Delta G$, formed by subtracting the AdS vacuum two-point function from the thermal two-point function built as an imaginary-time sum over copies of the vacuum propagator; the renormalized stress-energy tensor difference is then the coincidence limit of this function and its second derivatives. The scalar field obeys Dirichlet boundary conditions (the field vanishes at the AdS boundary) so that no energy flows out. On the kinetic-theory side, the RKT-SET comes from integrating the Bose-Einstein distribution with the local redshifted temperature over momenta. The comparison is done in the thermometer frame, a decomposition that splits any stress tensor into energy density, isotropic pressure, heat flux, and anisotropic stress; in RKT the heat flux and anisotropic stress vanish identically, so their nonzero QFT values are the measure of quantum effects.","core_discovery":"On the paper's own terms, for a massless, conformally coupled scalar field on global three- and four-dimensional AdS with angular speed $|\\Omega|$ less than the inverse AdS radius (so no speed-of-light surface forms), the difference between the rigidly-rotating thermal and vacuum renormalized stress-energy tensors is traceless, conserved, and decomposes in the thermometer frame into an energy density, pressure, a single azimuthal heat flux, and an anisotropic stress. At high temperature this QFT result is well approximated by the RKT perfect-fluid tensor, whose local temperature follows the gravitational redshift factor; at low temperature RKT overestimates the energy density. In contrast to rigidly rotating fermion states, where the energy-density maximum moves outward as rotation increases, the scalar energy density retains its maximum at the origin. The heat flux is always directed opposite to the rotation, and in four dimensions the anisotropic stress has a component $\\Pi_{(\\rho)(\\theta)}$ that vanishes for fermions.","pith_inferences":["If the lagging heat flux survives backreaction, a rotating quantum state on AdS would slowly transport angular momentum outward, so a stationary quantum-corrected soliton would need a compensating mechanism at the boundary; this is a testable consequence the paper does not develop.","The construction relies on $|\\Omega| < 1$ to avoid a speed-of-light surface; a natural extension is to probe the fate of the heat flux and the vacuum identity as $|\\Omega|$ approaches 1 from below.","The comparison between scalar and fermion stress tensors on identical AdS backgrounds isolates spin-rotation coupling; a matched calculation with identical temperature and angular speed would quantify how much of the anisotropic stress is due to spin.","The boundary-condition dependence could be probed by repeating the thermal subtraction with Neumann or other boundary conditions, since the paper's Dirichlet choice is motivated by prior comparison with kinetic theory."],"forward_implications":["At high temperature, all rotation effects on the scalar stress-energy tensor are captured by the classical gas description; any discrepancy is a low-temperature or boundary phenomenon.","The always-negative azimuthal heat flux means a rigidly rotating thermal scalar state does not co-rotate with the frame; the radiation lags, giving a concrete signature of quantum rotation.","The energy-density maximum at the origin is stable against rotation for scalars, unlike the fermion case, so scalar thermal states remain centered even for angular speeds near $|\\Omega| = 1$.","In four dimensions, rotation generates pressure-deviator components such as $\\Pi_{(\\rho)(\\theta)}$ and $\\Pi_{(\\varphi)(\\varphi)} - \\Pi_{(\\theta)(\\theta)}$ that vanish both without rotation and in kinetic theory; these are direct quantum rotational signatures.","Because the QFT-RSET is traceless and conserved, it is a ready source term for backreaction; the paper proposes rotating quantum-corrected AdS solitons as the next step."],"supporting_citations":[{"why":"Identifies the rigidly-rotating vacuum state with the non-rotating AdS vacuum, the assumption that makes the thermal subtraction well defined.","marker":"[15, 16]"},{"why":"Supplies the vacuum stress-energy tensor for the conformally coupled scalar field in AdS and the renormalization background.","marker":"[17]"},{"why":"Gives the coincidence-limit formula that turns the difference Green function into the difference of renormalized stress-energy tensors.","marker":"[20]"},{"why":"Previous comparison of scalar and fermion quantum field theory with kinetic theory on non-rotating AdS, establishing the high-temperature approximation that this paper extends to rotation.","marker":"[4]"},{"why":"Shows how a physical boundary inside the speed-of-light surface permits rotating thermal states on Minkowski space, motivating the AdS boundary as the natural container.","marker":"[5]"},{"why":"Provides the rigidly-rotating fermion results on AdS whose outward-moving energy-density maximum is contrasted with the scalar's origin-centered maximum.","marker":"[9]"},{"why":"Gives the fermion stress tensor in rotating AdS states, the baseline against which the scalar's extra anisotropic-stress component is identified.","marker":"[10]"},{"why":"Supports choosing Dirichlet boundary conditions by showing which boundary-condition choice is best approximated by kinetic theory.","marker":"[19]"},{"why":"Defines the n-dimensional Bose-Einstein distribution function used to build the kinetic-theory stress-energy tensor.","marker":"[12]"},{"why":"Provides the non-rotating scalar stress tensor and pressure-deviator components used as the zero-rotation baseline and the starting point for quantum-corrected solitons.","marker":"[24]"}],"fun_headline_variants":["Rotating AdS heat flows opposite to spin","Quantum heat flux reverses direction on AdS","Scalar field heat current counter-rotates in AdS","AdS rotation flips quantum heat flow","Heat flux opposes rotation in AdS gas"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that the rigidly-rotating vacuum state is exactly the same as the non-rotating AdS vacuum, so subtracting the vacuum stress tensor removes all vacuum effects; if that identity fails for the Dirichlet boundary conditions used, the reported energy-density comparison and the sign and size of the heat flux would change.","fun_headline_variants_meta":{"raw":{"variants":["Rotating AdS heat flows opposite to spin","Quantum heat flux reverses direction on AdS","Scalar field heat current counter-rotates in AdS","AdS rotation flips quantum heat flow","Heat flux opposes rotation in AdS gas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000155,"raw_usage":{"total_tokens":1147,"prompt_tokens":810,"completion_tokens":337,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":426,"completion_tokens_details":{"reasoning_tokens":266}},"tokens_in":426,"tokens_out":337,"duration_ms":3902,"temperature":1.0,"reasoning_tokens":266,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:03:25.372225+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Directly compute the rigidly-rotating vacuum two-point function for the Dirichlet scalar field and compare it with the non-rotating AdS vacuum Green function; any nonzero difference at order $\\Omega^2$ would alter the subtracted stress-energy tensor and would appear as a change in the predicted heat flux.","supporting_citations":[{"cited_title":"Dirac fermions on an anti-de Sitter background","cited_arxiv_id":"1405.2215","evidence_quote":"Provides the rigidly-rotating fermion results on AdS whose outward-moving energy-density maximum is contrasted with the scalar's origin-centered maximum."},{"cited_title":"Boisseau, W","cited_arxiv_id":null,"evidence_quote":"Defines the n-dimensional Bose-Einstein distribution function used to build the kinetic-theory stress-energy tensor."},{"cited_title":"Quantum-corrected anti-de Sitter space-time","cited_arxiv_id":"2405.20422","evidence_quote":"Provides the non-rotating scalar stress tensor and pressure-deviator components used as the zero-rotation baseline and the starting point for quantum-corrected solitons."}],"review_version":1}