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arxiv: 2606.17149 · v1 · pith:BNLDT46Lnew · submitted 2026-06-15 · ✦ hep-th · gr-qc

Extended Supergravity Needs String Scale Cut-off

Ashoke Sen This is my paper

Pith reviewed 2026-06-27 02:59 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords BPS indexsupergravitystring theoryblack holesone-loop correctioncut-off scalesupersymmetryD-branes
0
0 comments X

The pith

Setting the ultraviolet cut-off to the string scale removes string-coupling dependence from the one-loop correction to the BPS index.

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

String compactifications to four dimensions with N=8, N=6 or N=4 supersymmetry admit BPS black holes carrying pure D-brane charges whose index must remain independent of the string coupling, since the coupling does not run. Explicit one-loop computations of this index via the gravitational path integral produce a result that depends on the ultraviolet cut-off scale. The paper shows that the dependence on the coupling vanishes exactly when the cut-off is taken at the string scale, restoring agreement with supersymmetry. The same cancellation occurs for type II strings on Calabi-Yau threefolds with vanishing Euler number.

Core claim

When the ultraviolet cut-off in the one-loop gravitational path integral is identified with the string scale, the resulting correction to the supersymmetric index of these BPS black holes loses all dependence on the string coupling, in agreement with the non-renormalization expected from extended supersymmetry.

What carries the argument

One-loop gravitational path integral for the BPS index evaluated with a string-scale ultraviolet cut-off.

If this is right

  • The index computed from the gravitational side matches the coupling-independent value required by supersymmetry.
  • Extended supergravity effective descriptions of these black holes become consistent only after the string-scale cut-off is imposed.
  • The same cancellation applies to type II compactifications on Calabi-Yau manifolds with zero Euler number.
  • For Calabi-Yau manifolds with non-zero Euler number the coupling dependence remains and requires separate resolution.

Where Pith is reading between the lines

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

  • Effective field theory treatments of black-hole indices in these backgrounds must adopt a string-scale cut-off to reproduce microscopic results.
  • The result suggests that any apparent renormalization of the index in extended supergravity is an artifact of using an incorrect cut-off.
  • Similar cut-off prescriptions could be tested in other supersymmetric compactifications where the index is known to be coupling-independent.

Load-bearing premise

The one-loop gravitational path integral captures the entire cut-off dependence of the index, with no additional contributions from stringy modes or higher-genus surfaces that would reintroduce coupling dependence.

What would settle it

An explicit two-loop or stringy-mode calculation that retains coupling dependence after the cut-off is fixed at the string scale would show the claim is incorrect.

read the original abstract

Many string compactifications down to four non-compact space-time dimensions with N=8, N=6 and N=4 supersymmetry have BPS black holes carrying pure D-brane charges and preserving four supersymmetries. The string coupling does not flow in these backgrounds and can be set to any arbitrary value. Therefore the supersymmetric index of these black holes must be independent of the string coupling. On the other hand, explicit computation of one loop correction to the index from gravitational path integral is sensitive to the choice of ultraviolet cut-off. We show that if the cut-off scale is chosen to be the string scale in accordance with the rules of string theory, then the dependence of the index on the string coupling disappears in accordance with the expectation from supersymmetry. Similar results are obtained for type II string theories compactified on Calabi-Yau manifolds with zero Euler number. For non-zero Euler number we encounter a puzzle that we discuss but do not fully resolve.

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

1 major / 0 minor

Summary. The manuscript claims that for string compactifications to N=8, N=6 and N=4 supergravity (and type II on Calabi-Yau threefolds with zero Euler number) the one-loop gravitational path-integral correction to the BPS index becomes independent of the string coupling once the ultraviolet cutoff is fixed at the string scale, in agreement with the supersymmetry expectation that the index cannot depend on a non-running coupling. For nonzero Euler number the authors report an unresolved puzzle.

Significance. If the result holds, the work supplies an explicit illustration that effective supergravity computations of BPS indices require a string-scale cutoff to match supersymmetry non-renormalization theorems. The concrete demonstration for the extended-supersymmetry cases and zero-Euler-number compactifications is a useful consistency check between the two frameworks.

major comments (1)
  1. [Abstract] Abstract: the central claim that the string-scale cutoff removes all coupling dependence is qualified by the explicit statement of an unresolved puzzle for nonzero-Euler-number Calabi-Yau compactifications. This indicates that the one-loop gravitational path integral does not universally exhaust the cutoff sensitivity, which bears directly on whether the result establishes the necessity of the string-scale cutoff in extended supergravity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for recognizing the value of our explicit consistency check between the gravitational path integral and supersymmetry non-renormalization theorems in the extended-supersymmetry cases. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the string-scale cutoff removes all coupling dependence is qualified by the explicit statement of an unresolved puzzle for nonzero-Euler-number Calabi-Yau compactifications. This indicates that the one-loop gravitational path integral does not universally exhaust the cutoff sensitivity, which bears directly on whether the result establishes the necessity of the string-scale cutoff in extended supergravity.

    Authors: We agree that the abstract already qualifies the result by noting the unresolved puzzle for nonzero-Euler-number Calabi-Yau threefolds. The manuscript's title, abstract, and body focus the central claim on extended supergravity (N=8, N=6, N=4) and zero-Euler-number compactifications, where the string-scale cutoff removes the coupling dependence from the one-loop correction to the BPS index. This matches the supersymmetry expectation that the index cannot depend on a non-running coupling. The nonzero-Euler puzzle is presented as an open issue outside the scope of the main result; it does not undermine the demonstration for the cases of extended supersymmetry. We are prepared to revise the abstract to make the scope even more explicit if the editor and referee consider it helpful. revision: partial

Circularity Check

0 steps flagged

No significant circularity; result is a consistency check using external string-theory cut-off rule

full rationale

The paper computes the one-loop gravitational correction to the BPS index and shows that its explicit string-coupling dependence vanishes precisely when the UV cut-off is set to the string scale. This choice is imported from string-theory rules rather than fitted inside the paper, and the target independence is taken from supersymmetry (string coupling does not flow). No equation redefines a quantity in terms of itself, no parameter is fitted to a subset and then relabeled a prediction, and no load-bearing step reduces to a self-citation chain. The derivation therefore remains self-contained against the stated external inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The argument rests on the domain assumption that the supersymmetric index must be coupling-independent and on the string-theory rule that the ultraviolet cut-off sits at the string scale; no free parameters or new entities are introduced.

axioms (2)
  • domain assumption Supersymmetric index of BPS black holes must be independent of string coupling when the coupling does not flow.
    Stated directly in the abstract as an expectation from supersymmetry.
  • domain assumption One-loop correction to the index computed from the gravitational path integral is sensitive to the ultraviolet cut-off.
    Basis for the explicit computation described in the abstract.

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discussion (0)

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Reference graph

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