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arxiv: 2606.31901 · v1 · pith:ZU4OKX6Pnew · submitted 2026-06-30 · ✦ hep-th · gr-qc

Exact Planar Black Hole in AdS-Einstein-Scalar Gravity with IR Emergent Nearly Conformal Fluid

Sangheon Yun This is my paper

Pith reviewed 2026-07-01 04:12 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords black braneAdS gravityscalar hairholographic RG flowconformal fluidABJM theoryscale symmetry breakingplanar black hole
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The pith

An exact planar black brane solution in Einstein-scalar gravity yields a boundary theory that breaks scale symmetry explicitly in the UV yet recovers conformal fluid behavior in the IR thermal limit.

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

The paper presents an exact analytic solution for a static plane-symmetric hairy black brane in four-dimensional Einstein gravity minimally coupled to a neutral scalar. This solution arises from a consistent truncation of type IIA supergravity and is characterized by two independent parameters. Thermodynamics are derived by treating the scalar hair parameter as independent, producing a generalized first law and satisfying the Euler relation. The dual three-dimensional boundary theory is deformed by a marginally relevant scalar operator that drives logarithmic RG flow, breaking scale symmetry at high energies while the infrared thermal limit exhibits the properties of a conformal fluid.

Core claim

The central claim is the existence of an exact analytic static plane-symmetric hairy black brane solution in AdS-Einstein-scalar gravity. Treating the scalar hair as an independent thermodynamic variable yields a generalized first law and verifies the Euler relation. The UV boundary theory is a three-dimensional QFT at finite temperature deformed by a marginally relevant scalar operator with logarithmic RG flow, exhibiting explicit scale-symmetry breaking at high energies but recovering conformal fluid behavior in the infrared thermal limit.

What carries the argument

The exact analytic plane-symmetric hairy black brane solution with two independent parameters, which encodes the RG flow from UV scale breaking to IR conformal behavior.

If this is right

  • The generalized first law holds when the scalar hair parameter is treated as an independent thermodynamic variable.
  • The Euler relation is satisfied by the thermodynamic quantities of the solution.
  • The boundary theory shows explicit scale symmetry breaking at high energies due to the marginally relevant operator.
  • The infrared thermal limit of the boundary theory recovers the behavior of a conformal fluid.

Where Pith is reading between the lines

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

  • The two-parameter family may permit studies of how the strength of UV deformation affects the approach to conformality.
  • Similar truncations could be examined in other holographic setups to test whether emergent IR conformality is generic.
  • The solution provides a concrete background for computing transport coefficients that interpolate between non-conformal and conformal regimes.

Load-bearing premise

The solution arises as a consistent truncation of type IIA supergravity whose low-energy limit captures the strongly coupled thermal dynamics of the ABJM theory.

What would settle it

Thermodynamic quantities computed from the solution failing to match those expected from the low-energy limit of the ABJM theory, or an explicit demonstration that the truncation is inconsistent.

read the original abstract

We study an exact analytic solution describing a static plane-symmetric hairy black brane in four-dimensional Einstein gravity minimally coupled to a neutral scalar, arising as a consistent truncation of the type IIA supergravity whose low-energy limit captures the strongly coupled thermal dynamics of the ABJM theory. The solution is characterized by two independent parameters. We perform the thermodynamic description by treating the scalar hair parameter as an independent variable, deriving the generalized first law and verifying the Euler relation. The UV boundary theory is a three-dimensional QFT at finite temperature deformed by a marginally relevant scalar operator with logarithmic RG flow. The boundary theory exhibits explicit scale-symmetry breaking at high energies but recovers the behavior of a conformal fluid in the infrared thermal limit.

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

2 major / 1 minor

Summary. The manuscript presents an exact analytic solution for a static plane-symmetric hairy black brane in four-dimensional Einstein gravity minimally coupled to a neutral scalar field, obtained as a consistent truncation of type IIA supergravity relevant to the ABJM theory. The solution depends on two independent parameters. Thermodynamics are analyzed by treating the scalar hair parameter as independent, yielding a generalized first law and verification of the Euler relation. The dual three-dimensional QFT is deformed by a marginally relevant scalar operator with logarithmic RG flow; the boundary theory is claimed to exhibit explicit scale-symmetry breaking at high energies while recovering the behavior of a conformal fluid in the infrared thermal limit.

Significance. If the analytic solution, thermodynamic relations, and RG interpretation are correct, the work would supply a rare exact holographic example of emergent IR near-conformality arising from a UV-deformed theory, with potential utility for modeling finite-temperature ABJM dynamics. The provision of an exact solution with two free parameters and explicit thermodynamic identities is a technical strength.

major comments (2)
  1. [Abstract] Abstract: The assertion that the boundary theory exhibits explicit scale-symmetry breaking at high energies but recovers conformal fluid behavior in the infrared contradicts standard RG expectations for a marginally relevant operator (Δ=3). For such an operator the beta function drives the coupling away from the UV fixed point, producing stronger explicit breaking in the IR and approximate conformality only in the UV. This reversal directly undermines the central claim of IR emergent nearly conformal fluid behavior and requires explicit resolution (e.g., via the beta-function derivation or the precise identification of the operator dimension and flow direction).
  2. [Abstract] Abstract and § (thermodynamic section): The thermodynamic analysis treats the scalar hair parameter as an independent variable to obtain the generalized first law and Euler relation. However, the manuscript must demonstrate that this parameter is not fixed by the equations of motion or by the consistent truncation; otherwise the two-parameter counting and the independence assumption become circular when deriving the IR limit.
minor comments (1)
  1. [Abstract] The abstract refers to 'logarithmic RG flow' without specifying the coefficient or the explicit form of the beta function; a brief equation or reference in the main text would clarify the marginally relevant character.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive major comments. We address each point below and will revise the manuscript accordingly where the comments identify areas for clarification or correction.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the boundary theory exhibits explicit scale-symmetry breaking at high energies but recovers conformal fluid behavior in the infrared contradicts standard RG expectations for a marginally relevant operator (Δ=3). For such an operator the beta function drives the coupling away from the UV fixed point, producing stronger explicit breaking in the IR and approximate conformality only in the UV. This reversal directly undermines the central claim of IR emergent nearly conformal fluid behavior and requires explicit resolution (e.g., via the beta-function derivation or the precise identification of the operator dimension and flow direction).

    Authors: We agree with the referee that the abstract phrasing reverses the standard RG flow direction for a marginally relevant operator. The UV is the approximate fixed point, with the deformation inducing stronger explicit breaking toward the IR. We will revise the abstract to correct this wording and will add an explicit derivation of the beta function (showing the logarithmic running) together with a clarification of the operator dimension. At the same time, the exact black-brane solution still exhibits thermodynamic quantities that approach those of a conformal fluid in the low-temperature (thermal IR) limit; we will strengthen the discussion of this emergent behavior without claiming it contradicts the RG flow. This revision addresses the concern while preserving the central technical result. revision: yes

  2. Referee: [Abstract] Abstract and § (thermodynamic section): The thermodynamic analysis treats the scalar hair parameter as an independent variable to obtain the generalized first law and Euler relation. However, the manuscript must demonstrate that this parameter is not fixed by the equations of motion or by the consistent truncation; otherwise the two-parameter counting and the independence assumption become circular when deriving the IR limit.

    Authors: The two-parameter family is obtained by direct integration of the equations of motion that follow from the consistent truncation; both the mass parameter and the scalar hair amplitude remain free after all constraints are imposed. We will add an explicit paragraph (or appendix subsection) verifying that the metric and scalar ansatz satisfy the full set of second-order ODEs identically for arbitrary values of the hair parameter (within the physical domain), confirming that the parameter is not fixed by the EOM or the truncation. This establishes the independence used in the thermodynamic analysis and removes any potential circularity. revision: yes

Circularity Check

0 steps flagged

No circularity: exact solution and thermodynamics are self-contained

full rationale

The paper derives an exact analytic black brane solution from the Einstein-scalar field equations as a consistent truncation, then applies standard thermodynamic relations by treating the two independent parameters (including scalar hair) as free variables to obtain the first law and Euler relation. No steps reduce a claimed prediction to a fitted input by construction, no load-bearing self-citations are invoked for uniqueness or ansatz, and the IR conformal fluid recovery is presented as a direct consequence of the solution's asymptotics rather than a redefinition of inputs. The derivation chain remains independent of the target claims.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the truncation assumption from type IIA supergravity and the existence of an exact solution with two independent parameters; no invented entities or additional free parameters are stated in the abstract.

free parameters (1)
  • scalar hair parameter
    Treated as an independent variable in the thermodynamic description.
axioms (1)
  • domain assumption The solution arises as a consistent truncation of type IIA supergravity capturing ABJM thermal dynamics
    Stated directly in the abstract as the origin of the model.

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discussion (0)

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