On the Scattering Phase for AdS_5 x S^5 Strings

TL;DR

The paper addresses the problem of determining the exact dressing phase for the worldsheet S-matrix of strings on AdS5 x S5 by enforcing crossing symmetry. It proposes a crossing-symmetric phase, expressed as sigma = exp(i theta) with a two-part theta = theta0 + theta1, where theta1 captures the Hernandez–Lopez one-loop contribution and theta0 provides a leading, classical-like term; a homogeneous piece delta theta is included to satisfy all crossing constraints. The authors argue, via analytic structure considerations and perturbative checks, that this phase reproduces known string-theory results and is consistent with crossing to several orders, though it does not fully align with giant-magnon scattering without the homogeneous term. They outline future work to derive the phase from first principles in string theory and to test weak-coupling behavior against gauge theory predictions. Overall, the work advances understanding of the AdS/CFT integrable structure by offering a concrete, crossing-symmetric dressing phase for the AdS5 x S5 worldsheet S-matrix.

Abstract

We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x S^5 apparently solving Janik's crossing relation.