A Crossing-Symmetric Phase for AdS_5 x S^5 Strings

TL;DR

This paper presents an all-order perturbative expression for the dressing phase of the AdS_5 x S^5 string S-matrix, revealing its analytic structure at finite coupling and matching known strong coupling data.

Contribution

It introduces a novel all-order perturbative formula for the dressing phase that satisfies crossing symmetry and connects strong and weak coupling regimes.

Findings

Matching with known strong coupling data

Recovery of giant magnon bound states as poles

Insights into the phase's analytic structure at finite coupling

Abstract

We propose an all-order perturbative expression for the dressing phase of the AdS_5 x S^5 string S-matrix at strong coupling. Moreover, we are able to sum up large parts of this expression. This allows us to start the investigation of the analytic structure of the phase at finite coupling revealing a few surprising features. The phase obeys all known constraints including the crossing relation and it matches with the known physical data at strong coupling. In particular, we recover the bound states of giant magnons recently found by Hofman and Maldacena as poles of the scattering matrix. At weak coupling our proposal seems to differ with gauge theory. A possible solution to this disagreement is the inclusion of additional pieces in the phase not contributing to crossing, which we also study.