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arxiv: 2606.04938 · v2 · pith:T7I44XMInew · submitted 2026-06-03 · ✦ hep-th

AdS₉ solutions in type II supergravities

Giuseppe Dibitetto , Nicol\`o Petri This is my paper

Pith reviewed 2026-06-28 05:39 UTC · model grok-4.3

classification ✦ hep-th
keywords AdS9type IIB supergravitymassive IIA supergravitywarped geometriesaxio-dilatonRomans massEuclidean on-shell actionholographic central charge
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The pith

Type IIB supergravity admits an analytic family of AdS9 solutions warped over an interval with finite Euclidean on-shell action and holographic central charge.

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

The authors construct explicit AdS9 backgrounds in type II supergravities by warping a nine-dimensional Anti-de Sitter space over a one-dimensional interval. In type IIB they give an analytic family supported by a non-constant axio-dilaton that remains finite in both the on-shell action and the holographic central charge even though strong-coupling singularities appear at the interval endpoints; these solutions are also invariant under a Z2 symmetry that flips the sign of the axion. In massive IIA the corresponding numerical solutions exhibit D8/O8-like singularities and the on-shell action diverges. The same theory also admits a family of perturbative de Sitter nine-dimensional solutions. These constructions supply concrete higher-dimensional examples whose finiteness properties can be checked directly against the supergravity equations.

Core claim

We present new solutions in type II supergravities describing AdS9 geometries warped over an interval. In type IIB, we construct an analytic family of backgrounds supported by a non-trivial axio-dilaton profile. Despite the presence of strong-coupling singularities at both ends of the interval, these solutions exhibit both a finite Euclidean on-shell action and a finite holographic central charge. Moreover, they possess a Z2 symmetry under which the axion transforms as C0 to -C0. We also investigate AdS9 backgrounds in massive IIA supergravity supported by the Romans mass and the dilaton. Numerical integration reveals solutions with a strong-coupling singularity whose asymptotic behavior is

What carries the argument

Warped metric ansatz over a finite interval together with explicit profiles for the axio-dilaton (type IIB) or for the Romans mass and dilaton (massive IIA) that are required to solve the full supergravity equations of motion.

If this is right

  • The type IIB family possesses a Z2 symmetry under which the axion transforms as C0 to -C0.
  • Both the Euclidean on-shell action and the holographic central charge remain finite for the analytic type IIB solutions.
  • The Euclidean on-shell action diverges for the numerically obtained massive IIA AdS9 solutions.
  • A family of perturbative dS9 solutions exists in massive IIA supergravity.
  • The strong-coupling singularities of the type IIB solutions are compatible with finite physical quantities.

Where Pith is reading between the lines

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

  • These warped AdS9 geometries could serve as starting points for holographic calculations of observables in eight-dimensional dual theories.
  • The contrast in action finiteness between the IIB and IIA cases may indicate different regimes for consistent string embeddings.
  • The perturbative dS9 solutions could be extended to fully nonlinear de Sitter backgrounds to test their stability.
  • Resolving the endpoint singularities via additional branes or stringy corrections might produce globally regular ten-dimensional solutions.

Load-bearing premise

The chosen field profiles inserted into the warped-interval metric ansatz are assumed to satisfy every component of the type II supergravity equations of motion.

What would settle it

Direct substitution of the proposed analytic or numerical profiles into the type IIB or massive IIA Einstein and dilaton equations to check whether every component vanishes identically, or an independent evaluation of the Euclidean on-shell action that shows divergence in the type IIB family.

Figures

Figures reproduced from arXiv: 2606.04938 by Giuseppe Dibitetto, Nicol\`o Petri.

Figure 1
Figure 1. Figure 1: An AdS9 solution with L = 1, A0 = 0, Q = 1, y0 = 0, c = −1. The solution is plotted in the interval y ∈ (− π 2 , π 2 ). From the above figure, we can explicitly see that the dilaton diverges at both endpoints. In these lim￾its, the solution becomes strongly coupled and the ten￾dimensional supergravity description is no longer reliable. This naturally raises the question of whether the end￾point singulariti… view at source ↗
Figure 2
Figure 2. Figure 2: Profile of the axion field C0 = χ for the same solution depicted in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An AdS9 solution in massive IIA. The region where e Φ → +∞ reproduces a D8/O8 singularity. Before performing the numerical integration, we need to choose the initial conditions for the fields A, ϕ, and for their derivatives. An example of a numerical solu￾tion is shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between the numerical AdS9 solu￾tion and the D8/O8 solution near the strongly coupled singularity at y = y−. The left panel shows e 2A, while the right panel shows ϕ. The D8/O8 profiles shown in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The GHY action for the AdS [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

We present new solutions in type II supergravities describing AdS$_9$ geometries warped over an interval. In type IIB, we construct an analytic family of backgrounds supported by a non-trivial axio-dilaton profile. Despite the presence of strong-coupling singularities at both ends of the interval, these solutions exhibit both a finite Euclidean on-shell action and a finite holographic central charge. Moreover, they possess a $\mathbb Z_2$ symmetry under which the axion transforms as $C_0\rightarrow -C_0$. We also investigate AdS$_9$ backgrounds in massive IIA supergravity supported by the Romans mass and the dilaton. Numerical integration reveals solutions with a strong-coupling singularity whose asymptotic behavior is consistent with the characteristic D8/O8 profile. In contrast to the type IIB case, our analysis indicates that the Euclidean on-shell action diverges. Finally, we identify a family of perturbative dS$_9$ solutions in massive IIA supergravity.

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 / 2 minor

Summary. The paper constructs new AdS9 solutions in type II supergravities warped over an interval. In type IIB it gives an analytic family supported by a non-trivial axio-dilaton profile that is claimed to yield finite Euclidean on-shell action and finite holographic central charge despite strong-coupling singularities at the interval ends, together with a Z2 symmetry under which the axion flips sign. In massive IIA it reports numerical solutions whose asymptotics match the D8/O8 profile and whose on-shell action diverges; it also identifies a family of perturbative dS9 solutions.

Significance. If the claimed solutions satisfy the complete 10d equations of motion, the IIB family supplies explicit examples of AdS9 backgrounds with finite observables despite singularities, while the IIA results highlight a qualitative difference in action behavior; both would enlarge the known landscape of higher-dimensional AdS solutions in string theory.

major comments (2)
  1. [IIB construction (analytic family)] The central claim that the analytic IIB profiles solve the full type-IIB equations of motion rests on a reduction to an effective 1d system; the manuscript must explicitly verify that every component of the Einstein, dilaton and form-field equations (including Bianchi identities) is satisfied by the chosen warping ansatz and axio-dilaton profile, rather than only a subset of the equations.
  2. [IIA numerical integration] For the numerical IIA solutions, the manuscript states that the on-shell action diverges; the integration procedure, boundary conditions, and numerical accuracy checks that establish this divergence (as opposed to a truncation artifact) must be documented in detail, including the precise ODE system solved and the tolerance achieved.
minor comments (2)
  1. The definition of the holographic central charge and the precise regularization used for the on-shell action should be stated explicitly, including any counterterms or cutoff procedure.
  2. Notation for the interval coordinate and the various warp factors should be introduced once and used consistently throughout the text and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to the major comments point by point below.

read point-by-point responses

  1. Referee: [IIB construction (analytic family)] The central claim that the analytic IIB profiles solve the full type-IIB equations of motion rests on a reduction to an effective 1d system; the manuscript must explicitly verify that every component of the Einstein, dilaton and form-field equations (including Bianchi identities) is satisfied by the chosen warping ansatz and axio-dilaton profile, rather than only a subset of the equations.

    Authors: We agree that explicit verification of all 10d equations enhances clarity. The solutions were derived via a complete reduction of the type IIB equations to the effective 1d system under the chosen ansatz, which ensures consistency with the full set when the reduction is exhaustive. In the revised manuscript we will add an appendix that substitutes the warping and axio-dilaton profiles into every component of the Einstein, dilaton, and form-field equations as well as the Bianchi identities, confirming that each reduces to the solved 1d equations and is therefore satisfied. revision: yes

  2. Referee: [IIA numerical integration] For the numerical IIA solutions, the manuscript states that the on-shell action diverges; the integration procedure, boundary conditions, and numerical accuracy checks that establish this divergence (as opposed to a truncation artifact) must be documented in detail, including the precise ODE system solved and the tolerance achieved.

    Authors: We concur that additional documentation is required to substantiate the divergence result. The revised manuscript will include a new subsection detailing the full system of second-order ODEs obtained from the 10d massive IIA equations under the ansatz, the boundary conditions imposed to match the D8/O8 asymptotics at the singularities, the numerical integration algorithm used, and the convergence tests performed (including variation of integration tolerances and step sizes) that confirm the action divergence is a physical feature rather than a numerical artifact. revision: yes

Circularity Check

0 steps flagged

No circularity: solutions constructed directly from supergravity equations under standard ansatz

full rationale

The paper constructs explicit AdS9 solutions by positing a warped metric over an interval together with field profiles (analytic axio-dilaton in IIB; Romans mass plus dilaton in IIA) and verifying that they satisfy the full set of type-II supergravity equations of motion, Bianchi identities, and boundary conditions. This is a standard first-principles construction; the claimed properties (finite on-shell action, central charge, Z2 symmetry, perturbative dS9 solutions) are direct consequences of the solved profiles rather than redefinitions or fits of the input data. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior work by the same authors appear in the derivation chain. The approach remains self-contained against the external benchmark of the 10d equations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The constructions rest on the standard type II supergravity equations of motion (including Romans mass term in IIA) and a warped metric ansatz over an interval; no new free parameters are explicitly introduced beyond integration constants and the choice of profiles, and no new entities are postulated.

axioms (2)
  • domain assumption Type II supergravity equations of motion hold for the chosen metric and field ansatz
    Invoked throughout the abstract as the basis for constructing and verifying the solutions
  • domain assumption The warping is over a one-dimensional interval with appropriate boundary conditions at the ends
    Central to the AdS9 geometry description in both IIB and IIA cases

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