Single-valuedness of the AdS Veneziano amplitude

TL;DR

This paper investigates the structure of the AdS Veneziano amplitude in string theory, demonstrating that curvature corrections can be represented by single-valued functions, and computes higher-order corrections using this insight.

Contribution

It introduces a new constraint based on single-valued functions to compute curvature corrections in the AdS Veneziano amplitude, extending previous results.

Findings

First curvature correction matches the single-valued function form.

Computed the second curvature correction using the new constraint.

Confirmed the consistency of the amplitude with the single-valuedness property.

Abstract

We consider the Veneziano amplitude for the scattering of gluons in type IIB string theory on $AdS_5 \times S^5/\mathbb{Z}_2$ in the presence of D7 branes. On general grounds curvature corrections around flat space can be thought of as arising from the extra insertion of soft gravitons. This naturally leads to an open string world-sheet representation with the extra insertion of single-valued functions evaluated on the real line. We check that the recently obtained first curvature correction is of this form and use this new constraint to compute the second curvature correction of the AdS Veneziano amplitude.