arxiv: 2604.21447 · v2 · submitted 2026-04-23 · ✦ hep-th · gr-qc

Recognition: 2 theorem links

· Lean Theorem

O(d,d) symmetric gravity and finite coupling holography

Umut G\"ursoy , Pedro Vicente Marto , Edwan Pr\'eau

Authors on Pith no claims yet

Pith reviewed 2026-05-13 08:00 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords O(d,d) symmetrycurvature correctionsblack braneholographyAdS5dilatonKasner exponentsasymptotic freedom

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The pith

O(d,d) symmetric curvature corrections leave the singularity inside AdS5 black branes unresolved but modify its Kasner exponents and can dynamically generate a negative cosmological constant at weak coupling when a dilaton is present.

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

The paper constructs asymptotically AdS5 black brane solutions in gravity theories that include an infinite series of curvature corrections respecting O(d,d) symmetry, which is argued to capture the classical NSNS sector of string theories. It shows that these corrections fail to remove the singularity behind the event horizon, although they change the way spacetime approaches that singularity through altered Kasner exponents. When a non-trivial dilaton field is included, a modest extension of the same corrections produces a negative cosmological constant dynamically in the region of small coupling. This mechanism supplies a possible dynamical origin for the AdS scale in a string-theoretic dual of QCD, thereby linking finite-coupling holography to asymptotic freedom.

Core claim

We construct asymptotically AdS5 black brane solutions in a theory of gravity with an infinite series of curvature corrections. The action is based on an O(d,d) symmetric ansatz which has been argued to describe the classical NSNS sector of string theories. We find that, for this general class of theories, the singularity behind the horizon is not resolved by the curvature corrections. The approach to the singularity is however generically modified, being characterized by different Kasner exponents. We also show that, in the presence of a non-trivial dilaton, a slight generalization of these types of curvature corrections can generate dynamically a negative cosmological constant in the small

What carries the argument

The O(d,d) symmetric ansatz for the gravitational action that includes an infinite series of curvature corrections, used both to construct the black brane geometries and to analyze the near-singularity region.

Load-bearing premise

The O(d,d) symmetric ansatz together with the chosen infinite series of curvature corrections correctly describes the classical NSNS sector of string theories.

What would settle it

An explicit string-theory computation at finite alpha-prime showing that the same curvature corrections resolve the inner singularity or fail to produce a negative cosmological constant with a non-trivial dilaton.

read the original abstract

We construct asymptotically AdS$_5$ black brane solutions in a theory of gravity with an infinite series of curvature corrections. The action is based on an $O(d,d)$ symmetric ansatz which has been argued to describe the classical NSNS sector of string theories. We find that, for this general class of theories, the singularity behind the horizon is not resolved by the curvature corrections. The approach to the singularity is however generically modified, being characterized by different Kasner exponents. We also show that, in the presence of a non-trivial dilaton, a slight generalization of these types of curvature corrections can generate dynamically a negative cosmological constant in the region of small coupling. This provides a mechanism through which asymptotic freedom could emerge in the hypothetical string dual of QCD.

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.

Desk Editor's Note private letter to a colleague

The paper constructs explicit AdS5 black brane solutions in an O(d,d)-invariant theory with an infinite curvature series, showing modified Kasner exponents without singularity resolution and a dilaton-driven negative cosmological constant at weak coupling.

read the letter

The core result is the construction of asymptotically AdS5 black brane solutions where the curvature corrections alter the Kasner exponents on approach to the singularity but leave it intact. With a non-trivial dilaton, a modest extension of the same corrections produces a negative cosmological constant in the weak-coupling region, which the authors link to a possible dynamical mechanism for asymptotic freedom in a string dual of QCD. That mechanism is the clearest new element here. The solutions themselves are presented as concrete outcomes of the O(d,d) ansatz plus the resummed action, and the Kasner modification is worked out explicitly enough to be checked by others in the same framework. The dynamical CC generation is a clean idea that follows from the equations once the dilaton is turned on. The main limitation is the infinite series itself. Near the singularity curvatures diverge, so every higher-order term becomes large and the resummation must be assumed to remain a valid effective description all the way down. The paper does not supply convergence checks or an independent argument that the series matches string theory once curvatures exceed the string scale. That assumption carries the load-bearing claims about both the unmodified singularity and the generated cosmological constant. The O(d,d) ansatz is taken from prior literature rather than re-derived, which is standard but means the work stands or falls on how well that ansatz captures the NSNS sector at finite coupling. This is for people already working on string-corrected gravity, O(d,d) models, or holographic QCD at finite coupling. A reader who wants explicit solutions and a concrete mechanism will find usable material, while someone looking for a fully controlled string derivation will see the gap at strong curvature. The constructions are specific enough and the logic is traceable enough that it should go to peer review rather than desk rejection; referees will need to press on the validity of the resummed action near the singularity, but the paper supplies enough to make that discussion worthwhile.

Referee Report

2 major / 1 minor

Summary. The paper constructs asymptotically AdS5 black brane solutions in a theory of gravity with an infinite series of curvature corrections based on an O(d,d) symmetric ansatz argued to describe the classical NSNS sector of string theories. It reports that the singularity behind the horizon is not resolved by these corrections, though the approach to the singularity is modified with different Kasner exponents. With a non-trivial dilaton, a slight generalization of the curvature corrections is shown to dynamically generate a negative cosmological constant in the small-coupling region, offering a potential mechanism for asymptotic freedom in a hypothetical string dual of QCD.

Significance. If the central results hold, the work provides a concrete example of how resummed higher-curvature corrections in an O(d,d)-invariant framework alter near-singularity behavior without resolving it, and supplies a dynamical origin for a negative cosmological constant relevant to finite-coupling holography. The structured inclusion of an infinite series and the explicit black-brane solutions constitute a technical advance over purely perturbative treatments.

major comments (2)

[Main results on black-brane solutions and singularity approach] The claims that curvature corrections do not resolve the singularity and only modify Kasner exponents rest on the equations of motion obtained from the resummed infinite series. Near the singularity curvature invariants diverge, so every higher-order term becomes non-perturbative; the manuscript must demonstrate that the resummed effective action remains a consistent description in this regime (e.g., by showing convergence of the series or consistency with string-scale physics). This assumption is load-bearing for both the non-resolution statement and the Kasner-exponent analysis.
[Dilaton-dependent cosmological-constant generation] The dynamical generation of a negative cosmological constant via a slight generalization of the curvature corrections in the presence of a non-trivial dilaton likewise depends on the same resummed action. The manuscript should specify the precise form of the generalization, verify that it preserves the O(d,d) symmetry, and confirm that the resulting equations remain well-defined when the dilaton varies.

minor comments (1)

All explicit equations of motion, the precise form of the infinite series, and the ansatz for the black-brane metric should be displayed in the main text rather than relegated to appendices, to allow direct verification of the Kasner-exponent calculations.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading and constructive comments. We address each major point below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: The claims that curvature corrections do not resolve the singularity and only modify Kasner exponents rest on the equations of motion obtained from the resummed infinite series. Near the singularity curvature invariants diverge, so every higher-order term becomes non-perturbative; the manuscript must demonstrate that the resummed effective action remains a consistent description in this regime (e.g., by showing convergence of the series or consistency with string-scale physics). This assumption is load-bearing for both the non-resolution statement and the Kasner-exponent analysis.

Authors: We acknowledge that the validity of the resummed O(d,d)-invariant action in the strong-curvature regime near the singularity requires explicit discussion. Our solutions are exact within the framework of the resummed effective action derived from the O(d,d) ansatz, which is motivated by the classical NSNS sector and permits non-perturbative resummation. The non-resolution of the singularity and the modified Kasner exponents follow directly from integrating the resulting equations of motion. We agree that a demonstration of series convergence or full string-scale consistency lies beyond the effective-theory scope of this work. In the revision we will add a dedicated subsection on the regime of validity, clarifying the assumptions and limitations of the model while preserving the reported results as exact within this framework. revision: partial
Referee: The dynamical generation of a negative cosmological constant via a slight generalization of the curvature corrections in the presence of a non-trivial dilaton likewise depends on the same resummed action. The manuscript should specify the precise form of the generalization, verify that it preserves the O(d,d) symmetry, and confirm that the resulting equations remain well-defined when the dilaton varies.

Authors: We agree that the generalization must be specified explicitly. In the revised manuscript we will provide the precise form of the dilaton-dependent modification to the curvature terms. This generalization is constructed so that the full action remains invariant under O(d,d) transformations by ensuring each correction transforms covariantly. We have checked that the resulting equations of motion are well-defined and consistent for a varying dilaton; the O(d,d) structure prevents the appearance of inconsistent or singular terms. These details, together with the verification, will be added to the text and to an appendix containing the explicit field equations. revision: yes

standing simulated objections not resolved

A rigorous proof of convergence of the infinite series when curvature invariants diverge, which would require non-perturbative string-theory input beyond the effective O(d,d) framework employed here.

Circularity Check

0 steps flagged

No circularity: solutions derived from stated action without reduction to fitted inputs or self-citation chains

full rationale

The paper constructs asymptotically AdS5 black brane solutions from an O(d,d)-invariant action with an infinite curvature series. The central claims (unresolved singularity with modified Kasner exponents; dynamical negative CC from dilaton) follow directly from solving the equations of motion obtained from that action. The O(d,d) ansatz is imported from prior literature as an assumption, not derived or fitted within the paper to the target results. No parameter is tuned to the singularity behavior or CC value, and no self-citation is invoked as a uniqueness theorem that forces the outcome. The derivation chain is therefore self-contained against the chosen action and ansatz; external validity of the resummed series is a separate question of applicability, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the O(d,d) ansatz and the chosen infinite series of curvature corrections; no explicit free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption O(d,d) symmetric ansatz describes the classical NSNS sector of string theories
Invoked as the basis for the action in the abstract.

pith-pipeline@v0.9.0 · 5433 in / 1289 out tokens · 42590 ms · 2026-05-13T08:00:17.776189+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The action is based on an O(d,d) symmetric ansatz... F(DS) = -c1 tr[DS²] - ∑ α'^{k-1} ∑_{P∈Part(k,2)} ck,P ∏ tr[DS^{2m}] (2.7)
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Kasner exponents... pt= (2-α)/(8-α), px=2/(8-α) (3.35); singularity not resolved (3.41)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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