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arxiv: 2603.28880 · v3 · submitted 2026-03-30 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Holographic two-point functions of heavy operators revisited

Prokopii Anempodistov
Authors on Pith no claims yet

Pith reviewed 2026-05-14 00:48 UTC · model grok-4.3

classification ✦ hep-th
keywords holographytwo-point functionsgiant gravitonsD3-brane actionboundary termsBPS operatorssupergravityN=4 SYM
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The pith

The D3-brane action requires additional boundary terms to compute holographic two-point functions of heavy operators correctly.

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

This paper examines how to compute two-point correlation functions of heavy chiral primary operators in a strongly coupled gauge theory using gravity in higher dimensions. It focuses on operators whose scaling dimensions are proportional to the number of colors or its square, corresponding to giant graviton configurations or bubbling geometries. The key proposal is that the standard brane action needs extra boundary terms to properly define the variational problem, and once included, the on-shell action directly gives the correct two-point function from the gauge theory side. This approach also extends to calculating correlators in more complex supergravity backgrounds by evaluating a specific boundary term in the pseudo-action.

Core claim

The central claim is that the D3-brane action for the giant gravitons and their BPS counterparts must include additional boundary terms derived from the path integral to ensure the variational problem is well-posed, and that the on-shell value of this corrected action reproduces the two-point functions of the corresponding gauge theory operators. For operators with scaling dimension scaling as N squared, the two-point function is obtained from the Gibbons-Hawking-York boundary term in the Type IIB pseudo-action evaluated in the bubbling geometry background.

What carries the argument

Additional boundary terms in the D3-brane action derived from the path integral to ensure a well-defined variational problem.

Load-bearing premise

That the proposed additional boundary terms arise naturally from the path integral, make the variational problem well-defined, and allow the on-shell action to directly reproduce the gauge theory two-point function.

What would settle it

A direct computation of the two-point function with the standard D3-brane action without the added terms yields a result that does not match the gauge theory expectation, while the version with the terms also fails to match after evaluation.

Figures

Figures reproduced from arXiv: 2603.28880 by Prokopii Anempodistov.

Figure 1
Figure 1. Figure 1: The giant graviton profile in the global [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The dual giant graviton profile in the Poincar´e coordinates. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

In this paper we investigate the holographic computation of the two-point functions of $\frac{1}{2}$-BPS chiral primary operators with scaling dimensions $\Delta \sim N$ or $\Delta \sim N^2$ in $\mathcal{N}=4$ $SU(N)$ SYM using Type IIB supergravity. First we consider giant graviton operators, resolving ambiguities in the previous literature on holographic computation of the two-point function, and make a new proposal for this calculation. We argue that the D3-brane action for the giant gravitons (as well as for their $\frac{1}{4}$- and $\frac{1}{8}$-BPS counterparts) should contain additional boundary terms which arise naturally from the path integral and which are required to make the variational problem well-defined. We derive the form of these terms and show that the corrected action has an on-shell value that reproduces the two-point function of the gauge theory operators. Then we consider operators with $\Delta \sim N^2$ and calculate the two-point function by evaluating the Gibbons-Hawking-York boundary term in the Type IIB pseudo-action in the Lin-Lunin-Maldacena bubbling geometry background.

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 investigates holographic two-point functions of heavy 1/2-BPS chiral primary operators (Δ ∼ N and Δ ∼ N²) in N=4 SYM via Type IIB supergravity. For giant gravitons and their 1/4- and 1/8-BPS counterparts, it proposes additional boundary terms in the D3-brane action, derived from path-integral considerations to ensure a well-defined variational problem; the on-shell value of the corrected action is shown to reproduce the gauge-theory two-point functions. For Δ ∼ N² operators, the two-point function is computed by evaluating the Gibbons-Hawking-York boundary term in the Lin-Lunin-Maldacena bubbling geometries.

Significance. If the central claims hold, the work supplies a consistent holographic prescription for correlators of heavy operators, resolving prior ambiguities in the literature and extending the dictionary to bubbling geometries. The path-integral origin of the boundary terms and the explicit on-shell matching constitute a concrete technical advance for non-perturbative regimes of AdS/CFT.

major comments (2)
  1. [Section 3] The derivation of the additional boundary terms for the D3-brane action (presented as arising naturally from the path integral) is load-bearing for the resolution of ambiguities; explicit steps showing how these terms emerge independently of the final correlator value, together with the precise variational problem they correct, must be verified in detail.
  2. [Section 4, Eq. (4.12)] The claim that the on-shell value of the corrected action reproduces the gauge-theory two-point function exactly requires explicit comparison, including normalization constants and any residual supergravity contributions, against known results for small-N cases or limiting regimes.
minor comments (2)
  1. [Section 3.4] Notation for the 1/4- and 1/8-BPS cases should be unified with the 1/2-BPS giant-graviton discussion to avoid reader confusion when comparing the boundary-term derivations.
  2. [Introduction] The abstract and introduction refer to 'resolving ambiguities in the previous literature'; a brief table or paragraph summarizing the specific prior discrepancies addressed would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We appreciate the positive assessment of the significance of the work. Below we address the major comments point by point. We will incorporate the requested clarifications and comparisons into a revised version of the manuscript.

read point-by-point responses

  1. Referee: [Section 3] The derivation of the additional boundary terms for the D3-brane action (presented as arising naturally from the path integral) is load-bearing for the resolution of ambiguities; explicit steps showing how these terms emerge independently of the final correlator value, together with the precise variational problem they correct, must be verified in detail.

    Authors: We agree that Section 3 would benefit from a more expanded, self-contained derivation. In the revised manuscript we will insert a dedicated subsection that begins from the path-integral definition of the D3-brane partition function, isolates the boundary contributions required for a well-posed variational problem (specifically, the fixed embedding coordinates at the AdS boundary), and derives the additional terms without reference to the final two-point-function result. This will make the logical independence of the boundary-term construction explicit. revision: yes

  2. Referee: [Section 4, Eq. (4.12)] The claim that the on-shell value of the corrected action reproduces the gauge-theory two-point function exactly requires explicit comparison, including normalization constants and any residual supergravity contributions, against known results for small-N cases or limiting regimes.

    Authors: We acknowledge that the current presentation of Eq. (4.12) would be strengthened by direct numerical and analytic comparisons. In the revision we will add an appendix that (i) fixes the overall normalization by matching the leading large-N coefficient to the known gauge-theory result, (ii) verifies the expression in the small-N limit (N=2) where the giant-graviton operator reduces to a single-trace operator, and (iii) explicitly shows that residual bulk supergravity contributions vanish on-shell for the chosen boundary conditions. These checks will be presented alongside the existing on-shell evaluation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives additional boundary terms for the D3-brane action directly from path-integral requirements to ensure a well-defined variational problem, then verifies that the on-shell value of the corrected action reproduces the gauge-theory two-point function. This verification is presented as an independent consistency check rather than a definitional or fitted input. No load-bearing steps reduce by construction to the target correlator, no self-citations are invoked to justify uniqueness or ansatzes, and the central construction relies on standard holographic principles without renaming known results or smuggling assumptions. The chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard assumptions of Type IIB supergravity, the AdS/CFT dictionary, and variational principles in brane actions, with the novel element being the path-integral origin of boundary terms.

axioms (2)
  • domain assumption The variational problem for the D3-brane action is ill-defined without additional boundary terms that arise from the path integral.
    Central to the giant graviton section; invoked to justify the new proposal.
  • domain assumption The on-shell value of the corrected brane action equals the two-point function of the dual gauge theory operators.
    Standard holographic identification applied to the corrected action.

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discussion (0)

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Lean theorems connected to this paper

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

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Reference graph

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