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arxiv: 2605.30417 · v1 · pith:TMFZJZJNnew · submitted 2026-05-28 · ✦ hep-th · gr-qc

Logarithm of charge ratio in black hole entropy

Muktajyoti Saha , Ashoke Sen , P. Shanmugapriya This is my paper

Pith reviewed 2026-06-29 06:06 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords black hole entropylogarithmic correctionsBPS black holesstring compactificationscharge ratiossupersymmetric string theoryN=4 theoryN=8 theory
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The pith

Weakly coupled string theory reproduces the logarithmic black hole entropy corrections that depend on the ratio of electric to magnetic charges.

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

The paper sets out to compute from the macroscopic side the terms in the logarithmic correction to BPS black hole entropy that involve the logarithm of the ratio of electric charges to magnetic charges. This computation is feasible when electric charges are much larger than magnetic charges, which forces the attractor value of the string coupling to be small. A sympathetic reader would care because these ratio-dependent terms appear in microscopic counts, so matching them provides an independent test of the microscopic entropy formulas. The authors include four specific adjustments (string-scale cutoff, dilaton-dependent ultra-local measure, Kalb-Ramond field as the integration variable, and microcanonical ensemble) and obtain exact agreement with the known microscopic results in the N=4 and N=8 cases.

Core claim

When electric charges greatly exceed magnetic charges, the attractor mechanism produces a small string coupling that permits a reliable one-loop string computation of the ratio-dependent logarithmic corrections to the entropy of four-supercharge BPS black holes. After adopting the string scale as the ultraviolet cutoff, the ultra-local measure with its dilaton-dependent metric, the Kalb-Ramond two-form rather than its dual axion as the path-integral variable, and the microcanonical ensemble, the resulting macroscopic expressions match the microscopic logarithmic corrections exactly in N=4 and N=8 string compactifications; the same procedure is carried out for N=2 compactifications where micr

What carries the argument

The one-loop correction to black-hole entropy obtained from the string effective action, evaluated at the attractor value of the dilaton set by the charge ratio and with the four listed adjustments to cutoff, measure, variable, and ensemble.

If this is right

  • Exact numerical agreement is obtained with the known microscopic entropy formulas in N=4 and N=8 theories.
  • The same macroscopic procedure can be applied directly to N=2 theories where microscopic results remain unknown.
  • The path-integral measure employed is consistent with the BV formalism of string field theory.
  • Each of the four adjustments (string-scale cutoff, dilaton-dependent measure, choice of field variable, and ensemble) is required for the match to hold.

Where Pith is reading between the lines

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

  • The same adjustments to cutoff, measure, and ensemble may be needed in other string-theory entropy calculations that compare macroscopic and microscopic results.
  • The approach supplies a concrete way to generate predictions for the ratio-dependent logarithmic terms in any N=2 compactification once the microscopic counting is performed.
  • The explicit verification against the BV formalism suggests the measure choice is not ad hoc but follows from the underlying string field theory.

Load-bearing premise

Electric charges being much larger than magnetic charges makes the string coupling small enough for weakly coupled string theory to compute the logarithmic corrections reliably.

What would settle it

A microscopic computation in an N=4 or N=8 model that yields a different numerical coefficient for the log(electric charge over magnetic charge) term than the macroscopic result would falsify the agreement.

read the original abstract

Logarithmic correction to BPS black hole entropy, computed from microscopic description, often contains terms involving large ratios of charges, besides the logarithmic terms involving the overall scale of the charges. If the electric charges are much larger than the magnetic charges, then the attractor value of the string coupling is small and one might hope to use weakly coupled string theory to compute logarithmic corrections involving ratios of charges from the macroscopic side. We compute these for black holes in flat space-time, preserving four supercharges, in $\mathcal{N} = 2$, $\mathcal{N}=4$ and $\mathcal{N}=8$ supersymmetric string compactifications in four dimensions. We find perfect agreement with the microscopic results in $\mathcal{N}=4$ and $\mathcal{N}=8$ theories, for which the microscopic results are known. Various stringy and statistical mechanical effects become important in this analysis, including 1) use of the correct ultra-violet cut-off (string scale instead of Planck scale), 2) correct path integral measure (ultra-local measure with appropriate dilaton dependent metric), 3) use of the correct path integral variable (Kalb-Ramond 2-form instead of the dual axion) and 4) change of ensemble (from grand canonical to microcanonical). We also verify that the measure we use is consistent with what follows from the BV formalism of string field theory.

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 paper computes logarithmic corrections to BPS black hole entropy in four-dimensional N=2, N=4, and N=8 string compactifications, focusing on terms that depend on large ratios of electric to magnetic charges. It performs the computation from the macroscopic side in weakly coupled string theory (valid when electric charges dominate), incorporating a string-scale UV cutoff, an ultra-local dilaton-dependent path-integral measure, the Kalb-Ramond 2-form as the integration variable, and a switch to the microcanonical ensemble. The resulting expressions are reported to agree perfectly with known microscopic results for the N=4 and N=8 cases.

Significance. If the central computation holds, the work supplies a non-trivial consistency check between macroscopic and microscopic descriptions of sub-leading logarithmic entropy corrections in string theory. It explicitly validates the necessity of string-scale effects, the correct measure, and ensemble choice for reproducing charge-ratio logarithms, and confirms consistency of the measure with the BV formalism of string field theory. This strengthens the reliability of the macroscopic approach for BPS black holes.

minor comments (2)
  1. [Abstract] The abstract states 'perfect agreement' after listing four effects but does not indicate where in the manuscript the explicit matching expressions (before and after each adjustment) appear; a short cross-reference would improve readability.
  2. Notation for the charge ratio (e.g., how the large electric/magnetic ratio is denoted and normalized) should be introduced once in the introduction and used consistently thereafter.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, recognition of the significance of the consistency check, and recommendation to accept the manuscript. No major comments were raised.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper performs an explicit macroscopic computation of logarithmic corrections to BPS entropy using standard string-theory inputs (string-scale cutoff, ultra-local dilaton-dependent measure, Kalb-Ramond variable, microcanonical ensemble) whose motivations are stated independently of the target microscopic results. These choices are cross-checked against the BV formalism of string field theory rather than being tuned post-hoc to force agreement. The reported perfect match with known microscopic results in N=4 and N=8 theories therefore constitutes an external benchmark test rather than a reduction by construction; no self-definitional step, fitted-input prediction, or load-bearing self-citation chain is present in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The central claim of agreement rests on several technical domain assumptions about the path integral that are introduced to produce the match.

axioms (5)
  • domain assumption Electric charges much larger than magnetic charges implies small string coupling at the attractor, allowing weakly coupled string theory computation
    Stated directly in the abstract as the enabling condition
  • ad hoc to paper String scale (not Planck scale) is the correct UV cut-off
    Listed as one of the important effects required for agreement
  • ad hoc to paper Ultra-local measure with appropriate dilaton-dependent metric is the correct path integral measure
    Listed as one of the important effects required for agreement
  • ad hoc to paper Kalb-Ramond 2-form (not dual axion) is the correct path integral variable
    Listed as one of the important effects required for agreement
  • ad hoc to paper Microcanonical ensemble (not grand canonical) is the appropriate ensemble
    Listed as one of the important effects required for agreement

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discussion (0)

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Forward citations

Cited by 1 Pith paper

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  1. Extended Supergravity Needs String Scale Cut-off

    hep-th 2026-06 conditional novelty 5.0

    String-scale UV cut-off in the gravitational path integral removes string-coupling dependence from the BPS black hole index in extended supergravity, matching supersymmetry expectations for zero-Euler-number cases.

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