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arxiv: 2606.09769 · v1 · pith:U67HFAFMnew · submitted 2026-06-08 · ✦ hep-th · math-ph· math.MP

All-multiplicity monodromy and KLT relations for AdS string integrals

Maria Nocchi , Rodrigo Schmidt Pitombo , Aur\'elie Str\"omholm Sangar\'e , Yi-Xiao Tao This is my paper

Pith reviewed 2026-06-27 15:39 UTC · model grok-4.3

classification ✦ hep-th math-phmath.MP
keywords AdS string amplitudesmonodromy relationsKLT relationsmultiple polylogarithmsworldsheet integralstree-level amplitudesopen stringsclosed strings
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The pith

AdS string integrals satisfy monodromy relations and KLT factorisation at all multiplicities.

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

The paper introduces all-multiplicity building blocks for tree-level string amplitudes in AdS space. These blocks are formed by dressing the usual flat-space disc and sphere integrals with multivariable multiple polylogarithms for open strings and their single-valued versions for closed strings. The authors then derive that the open-string versions obey monodromy relations while the closed-string versions admit KLT factorisation. This construction extends earlier low-point results to arbitrary numbers of external legs. A reader would care because the relations supply recursive structure that could simplify explicit calculations of higher-point amplitudes in curved backgrounds.

Core claim

We propose and study all-multiplicity building blocks for tree-level string amplitudes in AdS. These are worldsheet integrals obtained by dressing the corresponding flat-space disc and sphere integrals with multivariable multiple polylogarithms and their single-valued analogues, respectively. We derive monodromy relations for the open-string building blocks and a KLT factorisation for their closed-string counterparts. This extends the non-commutative AdS uplift of lower-point flat-space structures to general n-point kinematics.

What carries the argument

All-multiplicity building blocks formed by dressing flat-space disc and sphere integrals with multivariable multiple polylogarithms (open) and single-valued analogues (closed).

If this is right

  • Monodromy relations hold for open-string AdS building blocks at any multiplicity.
  • Closed-string AdS building blocks admit KLT factorisation into open blocks.
  • The relations follow from the flat-space case once the polylogarithmic dressing is applied.
  • Non-commutative AdS structures extend consistently from low-point to arbitrary n-point kinematics.

Where Pith is reading between the lines

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

  • The construction may allow recursive evaluation of higher-point AdS amplitudes without recomputing the full integral each time.
  • It could link to holographic calculations where AdS string amplitudes appear in correlation functions.
  • Explicit checks at six or seven points would test whether the inheritance from flat space continues to hold.

Load-bearing premise

Dressing flat-space integrals with multivariable multiple polylogarithms yields valid AdS building blocks whose monodromy and KLT properties are inherited directly from the flat-space case.

What would settle it

Compute the five-point open-string AdS integral explicitly, apply the proposed monodromy operator, and check whether the result vanishes or reduces exactly as predicted by the flat-space relation.

read the original abstract

We propose and study all-multiplicity building blocks for tree-level string amplitudes in AdS. These are worldsheet integrals obtained by dressing the corresponding flat-space disc and sphere integrals with multivariable multiple polylogarithms and their single-valued analogues, respectively. We derive monodromy relations for the open-string building blocks and a KLT factorisation for their closed-string counterparts. This extends the non-commutative AdS uplift of lower-point flat-space structures to general $n$-point kinematics.

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

0 major / 1 minor

Summary. The paper proposes all-multiplicity building blocks for tree-level string amplitudes in AdS, obtained by dressing the corresponding flat-space disc and sphere integrals with multivariable multiple polylogarithms and their single-valued analogues. It derives monodromy relations for the open-string building blocks and a KLT factorisation for the closed-string counterparts, extending non-commutative AdS uplifts of lower-point flat-space structures to general n-point kinematics.

Significance. If the derivations are correct, the construction supplies a systematic all-multiplicity framework for AdS string integrals that preserves key flat-space relations under the dressing procedure. This would constitute a concrete technical advance for higher-point amplitudes in curved backgrounds and could serve as input for further studies of AdS/CFT string correlators.

minor comments (1)
  1. The abstract states that the relations are derived after defining the dressed integrals, but the provided information contains no explicit derivation steps, explicit checks at n>4, or verification that the dressing commutes with the monodromy/KLT operations; this prevents assessment of the central claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for the positive assessment of its potential significance. The report indicates an 'uncertain' recommendation but does not list any specific major comments. Accordingly, we have no individual points to address.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines new all-multiplicity AdS building blocks explicitly as dressed flat-space disc/sphere integrals using multivariable multiple polylogarithms (and single-valued analogues). It then states that monodromy relations for the open-string versions and KLT factorisation for the closed-string versions are derived from these objects. No quoted equations or steps reduce a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or definitional renaming. The central claims rest on the explicit construction and asserted derivation rather than on any load-bearing self-reference or ansatz smuggled via prior work. This is the normal case of a self-contained derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the mathematical properties of multivariable multiple polylogarithms allowing the dressing procedure to preserve monodromy and KLT structures for arbitrary multiplicity; no free parameters are introduced and no new entities with independent evidence are postulated.

axioms (1)
  • domain assumption Multivariable multiple polylogarithms and their single-valued analogues can be used to dress flat-space integrals while preserving the structures needed for monodromy and KLT relations at all multiplicities
    This is the core implicit premise of the proposal described in the abstract.
invented entities (1)
  • all-multiplicity AdS string integral building blocks no independent evidence
    purpose: To serve as the integrands for tree-level string amplitudes in AdS at arbitrary multiplicity
    Newly defined objects obtained by dressing flat-space integrals; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.1-grok · 5618 in / 1347 out tokens · 30776 ms · 2026-06-27T15:39:11.222345+00:00 · methodology

discussion (0)

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Reference graph

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