Bound State Scattering Simplified

TL;DR

This paper simplifies the bound state scattering matrix in AdS5/CFT4 integrable systems, revealing its pole structure, new relations, and properties like crossing symmetry, aiding in finite-size effect calculations and universal understanding.

Contribution

It presents a simplified form of the bound state scattering matrix, making its pole structure explicit and deriving new relations and an explicit inverse, enhancing computational and theoretical insights.

Findings

Simplified the bound state scattering matrix.

Made the pole structure of the matrix manifest.

Derived new relations between matrix elements and an explicit inverse.

Abstract

In the description of the AdS5/CFT4 duality by an integrable system the scattering matrix for bound states plays a crucial role: it was initially constructed for the evaluation of finite size corrections to the planar spectrum of energy levels/anomalous dimensions by the thermodynamic Bethe ansatz, and more recently it re-appeared in the context of the glueing prescription of the hexagon approach to higher-point functions. In this work we present a simplified form of this scattering matrix and we make its pole structure manifest. We find some new relations between its matrix elements and also present an explicit form for its inverse. We finally discuss some of its properties including crossing symmetry. Our results will hopefully be useful for computing finite-size effects such as the ones given by the complicated sum-integrals arising from the glueing of hexagons, as well as help towards understanding universal features of the AdS5/CFT4 scattering matrix.