The Dressing Factor and Crossing Equations

TL;DR

This paper uses integral representations and crossing equations to determine the dressing factor and bound state S-matrix in AdS_5xS^5 string theory, enabling the formulation of TBA equations for the mirror theory.

Contribution

It introduces a method to fix the dressing factor on the rapidity torus and derives a bound state S-matrix independent of internal structure, completing the TBA setup.

Findings

Successfully fixed the dressing factor using crossing equations.

Derived a bound state S-matrix independent of internal structure.

Provided the missing piece for TBA equations in the mirror theory.

Abstract

We utilize the DHM integral representation for the BES dressing factor of the world-sheet S-matrix of the AdS_5xS^5 light-cone string theory, and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus. The results obtained are further used, in conjunction with the fusion procedure, to determine the bound state dressing factor of the mirror theory. We convincingly demonstrate that the mirror bound state S-matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure. This welcome feature is in perfect parallel to string theory, where the corresponding bound state S-matrix has no bearing on bound state constituent particles as well. The mirror bound state S-matrix we found provides the final missing piece in setting up the TBA equations for the AdS_5xS^5 mirror theory.