Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

TL;DR

This paper studies the q-deformed S-matrix for excitations in AdS5 x S5 superstring theory, revealing momentum-dependent bound state properties and resolving crossing symmetry issues, with implications for string and relativistic limits.

Contribution

It introduces a detailed analysis of bound states in the q-deformed S-matrix, highlighting their momentum-dependent nature and resolving previous inconsistencies in the theory.

Findings

Bound states depend on momentum and transform between representations.

At low momentum, bound states are anti-symmetric and relate to Pohlmeyer solitons.

In the string limit, bound states become magnons, with no marginal instability in mirror kinematics.

Abstract

The investigation of the q deformation of the S-matrix for excitations on the string world sheet in AdS5 x S5 is continued. We argue that due to the lack of Lorentz invariance the situation is more subtle than in a relativistic theory in that the nature of bound states depends on their momentum. At low enough momentum |p|<E the bound states transform in the anti-symmetric representation of the super-algebra symmetry and become the solitons of the Pohlmeyer reduced theory in the relativistic limit. At a critical momentum |p|=E they become marginally unstable, and at higher momenta the stable bound states are in the symmetric representation and become the familiar magnons in the string limit as q->1. This subtlety fixes a problem involving the consistency of crossing symmetry with the relativistic limit found in earlier work. With mirror kinematics, obtained after a double Wick rotation, the bound state structure is simpler and there are no marginally unstable bound states.