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arxiv: 2604.09490 · v1 · submitted 2026-04-10 · ✦ hep-th

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The superconformal index and localizing higher derivative supergravity

Florian Gaar , Jerome P. Gauntlett , Jaeha Park , James Sparks
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:04 UTC · model grok-4.3

classification ✦ hep-th
keywords superconformal indexequivariant localizationhigher derivative supergravityAdS black holesrotating charged black holesCardy limitAdS/CFT correspondence
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The pith

Equivariant localization computes the exact on-shell action for supersymmetric rotating charged black holes in higher-derivative five-dimensional supergravity, matching the dual superconformal index in a Cardy-like limit.

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

This paper shows that equivariant localization applies to the on-shell action of supersymmetric D=5 AdS rotating charged black holes in higher-derivative supergravity theories. The resulting action produces an exact match with the superconformal index computed on the dual field theory side in the Cardy-like limit. A sympathetic reader would care because this supplies a direct, non-perturbative check of the AdS/CFT correspondence once higher-derivative corrections are included.

Core claim

We show how equivariant localization can be used to compute the on-shell action for supersymmetric D=5 AdS rotating, charged black holes in theories of supergravity with higher derivatives. An exact match with a dual field theory computation of the superconformal index in a Cardy-like limit is achieved.

What carries the argument

equivariant localization applied to the on-shell action of the higher-derivative supergravity theory

If this is right

  • The on-shell action of the black holes is obtained exactly without solving the full equations of motion.
  • Higher-derivative contributions to the action are included exactly by the localization procedure.
  • The gravitational result agrees with the field-theory index in the specified limit.

Where Pith is reading between the lines

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

  • The same localization step could be tested on other families of supersymmetric solutions in higher-derivative supergravity.
  • The exact match supplies a controlled setting in which to explore how higher-derivative terms affect holographic entropy and thermodynamics.

Load-bearing premise

Equivariant localization applies directly to the on-shell action without additional corrections from the higher-derivative terms or further assumptions about the supersymmetric locus.

What would settle it

A concrete mismatch between the localized gravitational on-shell action and the field-theory superconformal index for any choice of black-hole charges or angular momenta would show the claimed exact agreement does not hold.

read the original abstract

We show how equivariant localization can be used to compute the on-shell action for supersymmetric $D=5$ $AdS$ rotating, charged black holes in theories of supergravity with higher derivatives. An exact match with a dual field theory computation of the superconformal index in a Cardy-like limit is achieved.

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 / 2 minor

Summary. The paper shows that equivariant localization can be applied to evaluate the on-shell action of supersymmetric rotating charged AdS5 black holes in higher-derivative supergravity theories. It reports an exact numerical match between this localized gravitational action and the dual field-theory superconformal index evaluated in a Cardy-like limit.

Significance. If the central claim is correct, the result provides a non-trivial extension of localization techniques beyond two-derivative supergravity and supplies an exact test of AdS/CFT that incorporates higher-derivative corrections. Such a match would strengthen the case that the on-shell action of these black holes is captured by fixed-point contributions without additional corrections, offering a concrete handle on quantum corrections to black-hole thermodynamics in the presence of higher-derivative terms.

major comments (1)
  1. [The section deriving the localized on-shell action (around the rotating charged AdS black-hole solutions)] The central claim rests on the assumption that the supersymmetric locus (and therefore the fixed-point contributions to the localized action) remains identical to the two-derivative case once higher-derivative terms are included in the equations of motion. No explicit re-derivation of the Killing spinor equations or check for new fixed-point loci induced by the higher-derivative corrections is provided; without this verification the exact match cannot be regarded as controlled.
minor comments (2)
  1. [Lagrangian and action setup] The precise definition and normalization of the higher-derivative invariants should be stated explicitly (including any total-derivative or boundary contributions) so that the reader can confirm they are fully accounted for in the localization formula.
  2. [Results and comparison with field theory] A brief comparison table or explicit numerical values for the index and the localized action (for at least one choice of charges) would make the claimed exact match easier to inspect.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for raising this important point about the supersymmetric locus. We address the comment below and will revise the manuscript to incorporate the requested clarification.

read point-by-point responses

  1. Referee: [The section deriving the localized on-shell action (around the rotating charged AdS black-hole solutions)] The central claim rests on the assumption that the supersymmetric locus (and therefore the fixed-point contributions to the localized action) remains identical to the two-derivative case once higher-derivative terms are included in the equations of motion. No explicit re-derivation of the Killing spinor equations or check for new fixed-point loci induced by the higher-derivative corrections is provided; without this verification the exact match cannot be regarded as controlled.

    Authors: The supersymmetric locus is defined by the vanishing of the supersymmetry variations of the fermionic fields (primarily the gravitino), which determine the Killing spinor equations. In the higher-derivative supergravity theories considered here, the higher-derivative corrections are constructed as supersymmetric invariants that do not alter the supersymmetry transformation rules themselves. Consequently, the Killing spinor equations and the associated fixed-point loci for the rotating charged AdS5 black holes remain identical to the two-derivative case. While the equations of motion are modified by the higher-derivative terms, the on-shell action is evaluated precisely at the same supersymmetric configurations that solve the Killing spinor equations. To address the concern directly and make the argument fully explicit, we will add a dedicated subsection (or appendix) in the revised manuscript that re-derives the relevant Killing spinor equations including the higher-derivative contributions and confirms that no new fixed-point loci are introduced for the black-hole solutions under consideration. revision: yes

Circularity Check

0 steps flagged

No circularity: independent gravity localization matches separate field-theory index computation

full rationale

The derivation computes the on-shell action of higher-derivative D=5 supergravity via equivariant localization at the known supersymmetric AdS black-hole locus and obtains an exact numerical match to an independent dual-field-theory evaluation of the superconformal index in the Cardy-like limit. No step reduces a claimed prediction to a fitted parameter, self-defined quantity, or load-bearing self-citation; the localization formula is applied to the full higher-derivative Lagrangian without re-deriving the locus from the same data. The central result is therefore an external cross-check rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of equivariant localization to the higher-derivative on-shell action and on the validity of the Cardy-like limit for the index; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Equivariant localization theorem applies to the supersymmetric locus of the higher-derivative supergravity action
    Invoked to compute the on-shell action exactly
  • domain assumption The Cardy-like limit of the superconformal index captures the same quantity as the gravitational on-shell action
    Required for the exact match claim

pith-pipeline@v0.9.0 · 5342 in / 1220 out tokens · 38969 ms · 2026-05-10T17:04:38.094215+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Probing black holes with equivariant localization

    hep-th 2026-04 unverdicted novelty 7.0

    Equivariant localization computes probe D3-brane actions in uplifted Kerr-Newman-AdS5 supergravity backgrounds, reducing them to toric-data integrals for SCFT indices.

Reference graph

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