Generalized unitarity and the worldsheet S matrix in AdS_n x S^n x M^(10-2n)

TL;DR

This paper develops a generalized unitarity approach to compute the worldsheet S matrix in integrable string theories related to AdS/CFT dualities, providing explicit two-loop logarithmic terms and insights into higher-order structures.

Contribution

It introduces a method to calculate logarithmic contributions to the worldsheet S matrix at two loops using generalized unitarity, applicable to various AdS backgrounds, and analyzes higher-order features.

Findings

Explicit two-loop logarithmic terms computed for multiple AdS backgrounds.

Evidence for the absence of higher-order logarithms in the S matrix.

Confirmation of the exponentiation of the one-loop dressing phase.

Abstract

The integrability-based solution of string theories related to AdS(n)/CFT(n-1) dualities relies on the worldsheet S matrix. Using generalized unitarity we construct the terms with logarithmic dependence on external momenta at one- and two-loop order in the worldsheet S matrix for strings in a general integrable worldsheet theory. We also discuss aspects of calculations at higher orders. The S-matrix elements are expressed as sums of integrals with coefficients given in terms of tree-level worldsheet four-point scattering amplitudes. One-loop rational functions, not determined by two-dimensional unitarity cuts, are fixed by symmetry considerations. They play an important role in the determination of the two-loop logarithmic contributions. We illustrate the general analysis by computing the logarithmic terms in the one- and two-loop four-particle S-matrix elements in the massive worldsheet sectors of string theory in AdS_5 x S^5, AdS_4 x CP^3, AdS_3 x S^3 x S^3 x S^1 and AdS_3 x S^3 x T^4. We explore the structure of the S matrices and provide explicit evidence for the absence of higher-order logarithms and for the exponentiation of the one-loop dressing phase.