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arxiv: 2606.06596 · v1 · pith:6PT5Z4GOnew · submitted 2026-06-04 · ✦ hep-th

Instanton-Induced Closed-String Amplitudes in Minimal Superstring Theory at Subleading Order

Jyotirmoy Barman , Rishabh Kaushik , Raghu Mahajan , Chitraang Murdia , Ashoke Sen This is my paper

Pith reviewed 2026-06-27 23:55 UTC · model grok-4.3

classification ✦ hep-th
keywords minimal superstring theoryZZ instantonsDDK-KPZ scalingstring field theorydisk amplitudesannulus amplitudespicture changing operatorsvertical integration
0
0 comments X

The pith

String field theory regulation makes instanton-induced amplitudes in minimal superstring theory match DDK-KPZ scaling.

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

The paper computes the disk one-point function, disk two-point function, and annulus one-point function for the cosmological constant operator in type 0A and type 0B minimal superstring theories with ZZ instanton boundaries. Divergences in the two-point and one-point integrals are regulated using open-closed string field theory with specified picture-changing operator locations. After including all contributions and vertical integration, the amplitudes exactly match DDK-KPZ scaling expectations. This verifies the consistency of the string field theory approach for these non-perturbative effects.

Core claim

The disk one-point, disk two-point, and annulus one-point functions of the cosmological constant operator in minimal superstring theory with (1,1) ZZ instantons match the DDK-KPZ scaling predictions once all open-string channel divergences are properly regulated via string field theory vertices and vertical integration.

What carries the argument

Open-closed string field theory interaction vertices with chosen picture-changing operator positions, regulated by vertical integration to handle moduli space divergences from degenerations.

If this is right

  • The computed amplitudes are finite and agree with scaling laws.
  • The technical construction of interaction vertices applies to higher-dimensional cases like type IIB superstring.
  • All physical contributions are captured without additional boundary terms after the procedure.

Where Pith is reading between the lines

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

  • The same regulation method could resolve similar issues in ten-dimensional superstring amplitudes at subleading order.
  • Different choices for picture-changing locations might lead to equivalent physical results if vertical integration is applied consistently.
  • This approach may extend to computing higher-point functions or other operators in the theory.

Load-bearing premise

That the specified locations for picture-changing operators together with vertical integration account for every physical amplitude contribution without leftover degeneration effects.

What would settle it

An explicit computation of one of these amplitudes using an alternative regularization method that yields a result inconsistent with DDK-KPZ scaling would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.06596 by Ashoke Sen, Chitraang Murdia, Jyotirmoy Barman, Raghu Mahajan, Rishabh Kaushik.

Figure 1
Figure 1. Figure 1: The two Feynman diagrams contributing to the disk amplitude with two external closed [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Feynman diagrams contributing to the annulus amplitude with one external closed string. [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Moduli space of the annulus with a single closed-string insertion, showing its decomposition [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: This figure shows four Feynman diagrams contributing to the disk amplitude with one [PITH_FULL_IMAGE:figures/full_fig_p029_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Our choice of PCO locations in the different regions of moduli space for the disk two-point [PITH_FULL_IMAGE:figures/full_fig_p034_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The quantity Bβ is the sum of two contour integrals, one encircling each of the open-string insertions at −β and β. the region-(c) integrand is obtained by analytic continuation of the region-(d) integrand. Contribution from this region can be calculated by integrating over the region (c) using the (u, β) parameterization (4.20), expressing this in terms of q2 and β variables using (4.19), and finally usin… view at source ↗
read the original abstract

We compute the disk one-point function, the disk two-point function, and the annulus one-point function of the cosmological constant operator in the type 0A and type 0B minimal superstring theories with (1,1) ZZ instanton boundary conditions. The moduli-space integrals appearing in the disk two-point function and the annulus one-point function have divergences associated with open-string-channel degenerations, which must be regulated using open-closed string field theory. The definition of the string field theory interaction vertices requires a choice of locations for the picture-changing operators, which we specify in detail. After carefully taking into account all contributions, including those from vertical integration, we find that the results precisely match the expectations from DDK-KPZ scaling. Our technical results on the detailed construction of interaction vertices are a first step toward understanding the analogous quantities in the ten-dimensional type IIB superstring, where one also needs to understand how to treat the bosonic and fermionic collective coordinates at subleading order.

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

1 major / 1 minor

Summary. The manuscript computes the disk one-point function, the disk two-point function, and the annulus one-point function of the cosmological constant operator in type 0A and type 0B minimal superstring theories with (1,1) ZZ instanton boundary conditions. Divergences in the moduli-space integrals for the disk two-point and annulus one-point functions are regulated via open-closed string field theory vertices whose definition fixes picture-changing operator locations. After including all contributions (including vertical integration), the results are reported to match DDK-KPZ scaling expectations. Technical details on vertex construction are presented as a step toward analogous computations in ten-dimensional type IIB superstring theory.

Significance. If the central claim is robust, the work supplies a concrete check that SFT-regulated instanton amplitudes in minimal superstring theory reproduce the expected scaling at subleading order, together with explicit vertex constructions that may prove useful for handling bosonic and fermionic collective coordinates in higher-dimensional cases.

major comments (1)
  1. [Definition of SFT interaction vertices (as described in the abstract and relevant technical sections)] The section describing the definition of the string field theory interaction vertices: the claim that the final results match DDK-KPZ scaling after vertical integration rests on the assumption that the chosen PCO locations plus the vertical-integration procedure exhaust all physical contributions and leave no residual boundary or degeneration terms. No argument is supplied showing that the finite part of the amplitude is independent of this specific PCO placement; an alternative valid choice could shift the result and remove the reported agreement.
minor comments (1)
  1. [Abstract] The abstract asserts that 'all contributions were accounted for' and that results 'precisely match' DDK-KPZ scaling, but supplies no explicit equations, numerical values, or error estimates that would permit an independent cross-check of the matching.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Definition of SFT interaction vertices (as described in the abstract and relevant technical sections)] The section describing the definition of the string field theory interaction vertices: the claim that the final results match DDK-KPZ scaling after vertical integration rests on the assumption that the chosen PCO locations plus the vertical-integration procedure exhaust all physical contributions and leave no residual boundary or degeneration terms. No argument is supplied showing that the finite part of the amplitude is independent of this specific PCO placement; an alternative valid choice could shift the result and remove the reported agreement.

    Authors: We agree that the manuscript would benefit from an explicit statement on independence of the finite part from the PCO placement. The locations are fixed by the requirement that the vertices satisfy the picture number assignments and the homotopy relations of open-closed SFT. Vertical integration is defined to cover the full relevant moduli space, including all degenerations, so that any boundary contributions from alternative valid placements cancel. In the revised version we will add a concise paragraph making this independence argument explicit. The computed results and their agreement with DDK-KPZ scaling remain unchanged. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit SFT computation verified against external DDK-KPZ scaling

full rationale

The paper performs a direct moduli-space integration for the disk one-point, disk two-point, and annulus one-point functions, regulating open-string degenerations via explicitly constructed open-closed SFT vertices with chosen PCO locations and vertical integration. The final agreement with DDK-KPZ scaling is reported as the outcome of this calculation rather than an input or definitional constraint. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain; the technical construction of vertices is presented as independent content whose result is then compared to the known scaling law.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard conformal-field-theory integration over moduli space, the existence of a consistent open-closed string field theory that regulates open-string degenerations, and the assumption that the chosen picture-changing operator locations plus vertical integration exhaust all contributions. No free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Moduli-space integrals over disk and annulus surfaces with open-string-channel degenerations can be regulated by open-closed string field theory vertices.
    Invoked to handle the divergences mentioned in the abstract.
  • domain assumption A specific choice of picture-changing operator locations defines the interaction vertices unambiguously.
    Stated as required for the definition of the vertices.

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