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arxiv: 2605.18790 · v1 · pith:DJRPHNPFnew · submitted 2026-05-08 · ✦ hep-th

Matter one-loop logarithms and homogeneous TTNC scale response of Lifshitz black branes

Yingnan Xu , Shuangshuang Chu This is my paper

Pith reviewed 2026-05-20 23:39 UTC · model grok-4.3

classification ✦ hep-th
keywords Lifshitz black branesone-loop logarithmsTTNC scale responseheat kernel coefficientsconical entropyprobe fieldsWeyl Ward identity
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The pith

One-loop matter logarithms on Lifshitz black branes split into a smooth radial coefficient C1 that governs TTNC scale response and a horizon coefficient Wh that enters thermal entropy via C_therm = C1 + z L^2 Wh.

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

The paper computes the logarithmic one-loop corrections from probe scalar, Dirac, and Maxwell fields on a fixed neutral planar Lifshitz black-brane background. For each sector the log term factors into a smooth radial heat-kernel piece C1 that sources the homogeneous projection of the TTNC Weyl Ward identity and a conical horizon piece Wh. Closed expressions are supplied for C1, Wh and the combination C_therm in all three sectors, the gauge-field contact term in the conical entropy is isolated, and the z=1 relativistic limit is checked where the smooth response disappears while the standard horizon coefficient survives.

Core claim

The logarithmic one-loop matter contribution separates into a smooth radial heat-kernel contribution governed by C1 and a horizon-localized conical contribution governed by Wh, with the logarithmic thermal entropy controlled by C_therm = C1 + z L^2 Wh; explicit closed forms are obtained for the scalar, Dirac and Maxwell probe sectors together with the gauge-field contact term, and the smooth source response is shown to vanish in the relativistic planar z=1 limit while the horizon heat-kernel entropy coefficient remains.

What carries the argument

Separation of the logarithmic coefficient into smooth radial heat-kernel term C1 and horizon-localized conical term Wh, with C_therm = C1 + z L^2 Wh controlling entropy.

If this is right

  • The smooth coefficient C1 directly determines the source-induced homogeneous projection of the TTNC Weyl Ward identity.
  • The combination C_therm = C1 + z L^2 Wh supplies the logarithmic correction to the thermal entropy.
  • Closed expressions are now available for C1, Wh and C_therm in the scalar, Dirac and Maxwell sectors.
  • The Maxwell sector isolates a gauge-field contact contribution inside the conical entropy.
  • In the z=1 limit the smooth response vanishes while the standard horizon heat-kernel coefficient survives.

Where Pith is reading between the lines

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

  • These explicit coefficients could serve as benchmarks for numerical checks of holographic renormalization in non-relativistic settings.
  • Extending the same separation to back-reacting fields would test whether the probe approximation misses new logarithmic structures.
  • The z=1 vanishing result suggests a direct link between the smooth response and the non-relativistic deformation parameter that might appear in other scale-anomaly calculations.

Load-bearing premise

The quantum fields are treated as probes on the fixed neutral planar Einstein-Maxwell-dilaton Lifshitz background without back-reaction.

What would settle it

An explicit one-loop calculation for a probe scalar in the z=1 limit that produces a non-vanishing smooth source response in the TTNC Ward identity.

read the original abstract

We compute the logarithmic one-loop matter contribution to the thermodynamics and homogeneous TTNC scale response of a four-dimensional Lifshitz black brane. The background is the neutral planar member of the analytic Einstein--Maxwell--dilaton Lifshitz black-brane family, while the quantum fields are treated as probes: a real scalar with arbitrary mass and nonminimal curvature coupling, a four-component Dirac spinor, and an Abelian Maxwell field with its Faddeev--Popov ghosts. For each spin sector, the logarithmic coefficient separates into a smooth radial heat-kernel contribution, governed by $\mathcal{C}_1$, and a horizon-localized conical contribution, governed by $\mathcal{W}_h$. The smooth coefficient controls the source-induced homogeneous projection of the TTNC Weyl Ward identity, whereas the logarithmic thermal entropy is controlled by $\mathcal{C}_{\rm therm}=\mathcal{C}_1+zL^2\mathcal{W}_h$. We give closed expressions for $\mathcal{C}_1$, $\mathcal{W}_h$, and $\mathcal{C}_{\rm therm}$ in the scalar, Dirac, and Maxwell probe sectors, identify the gauge-field contact contribution in the conical entropy, and verify that the smooth source response vanishes in the relativistic planar $z=1$ limit while the standard horizon heat-kernel entropy coefficient remains.

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 / 2 minor

Summary. The manuscript computes the logarithmic one-loop matter contributions to the thermodynamics and homogeneous TTNC scale response of four-dimensional neutral planar Lifshitz black branes. Treating real scalars (with arbitrary mass and nonminimal coupling), Dirac spinors, and Abelian Maxwell fields (with ghosts) as probes on the fixed neutral planar Einstein-Maxwell-dilaton background, the work uses heat-kernel methods to separate the smooth radial contribution (controlled by C1) from the horizon-localized conical contribution (controlled by Wh). Closed expressions are given for C1, Wh, and the thermal combination C_therm = C1 + z L^2 Wh in each sector; the gauge-field contact term in the conical entropy is identified; and the smooth source response is shown to vanish in the z=1 relativistic limit while the standard horizon heat-kernel entropy coefficient is recovered.

Significance. If the derivations hold, the explicit closed-form results for the coefficients in the scalar, Dirac, and Maxwell sectors provide concrete benchmarks for quantum corrections in non-relativistic holography and for the TTNC Weyl Ward identity. The clean separation of smooth and conical pieces, the explicit insertion of the z factor into the thermal entropy, and the successful reduction to known relativistic coefficients when z=1 are notable strengths that increase the reliability and reusability of the computation. The probe approximation on the fixed background is the correct setup for this one-loop exercise.

minor comments (2)
  1. [Abstract] The abstract introduces C1, Wh, and C_therm without a one-sentence reminder of their physical roles (smooth source response versus thermal entropy); adding this would improve accessibility for readers outside the immediate subfield.
  2. A short paragraph or footnote recalling the definition of the TTNC Weyl Ward identity and its relation to the homogeneous scale response would help readers connect the coefficient C1 to the physical observable without consulting external references.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript, as well as for recommending acceptance. We are pleased that the referee highlighted the clean separation of smooth and conical heat-kernel contributions, the closed-form coefficients, the explicit z-dependence in the thermal entropy, and the successful reduction to the known z=1 results.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper carries out an explicit heat-kernel computation of one-loop logarithmic coefficients for probe scalar, Dirac, and Maxwell fields on a fixed neutral planar Einstein-Maxwell-dilaton Lifshitz black-brane background. It separates the smooth radial integral (governed by C1) from the horizon conical piece (governed by Wh), assembles the thermal combination C_therm = C1 + z L^2 Wh, and reduces the resulting closed expressions to the known z=1 relativistic values as a consistency check. All steps are performed directly from the background metric and standard heat-kernel techniques without fitting parameters to the target quantities, without load-bearing self-citations that presuppose the result, and without redefining inputs in terms of the outputs. The probe approximation is stated explicitly and is the appropriate setup for this calculation, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation relies on the standard heat-kernel expansion for one-loop determinants and the conical singularity method for horizon contributions; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Heat-kernel coefficients can be computed separately for smooth radial and horizon-localized conical parts on the Lifshitz background.
    Invoked when separating C1 from Wh in the abstract.
  • domain assumption Probe fields do not back-react on the fixed neutral planar Lifshitz black brane.
    Stated explicitly in the abstract as the treatment of quantum fields.

pith-pipeline@v0.9.0 · 5764 in / 1324 out tokens · 28913 ms · 2026-05-20T23:39:32.742899+00:00 · methodology

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Reference graph

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