Restoring Unitarity in the q-Deformed World-Sheet S-Matrix

TL;DR

This paper addresses the unitarity issues of the q-deformed world-sheet S-matrix in AdS5 x S5 string theory by transforming it into an IRF form, ensuring manifest unitarity and consistency with bootstrap principles.

Contribution

It introduces an IRF (vertex to IRF) transformation to restore manifest unitarity in the q-deformed S-matrix of the superstring, connecting it to the sine-Gordon theory and bootstrap equations.

Findings

IRF formulation makes unitarity manifest

S-matrix recovered in two limits matching known theories

Modified classical Yang-Baxter equation explains perturbative anomalies

Abstract

The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst this is a fascinating development the resulting S-matrix is not explicitly unitary. The problem has been known for a long time in the context of S-matrices related to quantum groups. A braiding relation often called "unitarity" actually only corresponds to quantum field theory unitarity when the S-matrix is Hermitian analytic and quantum group S-matrices manifestly violate this. On the other hand, overall consistency of the S-matrix under the bootstrap requires that the deformation parameter is a root of unity and consequently one is forced to perform the "vertex" to IRF, or SOS, transformation on the states to truncate the spectrum consistently. In the IRF formulation unitarity is now manifest and the string S-matrix and the S-matrix of the generalised sine-Gordon theory are recovered in two different limits. In the latter case, expanding the Yang-Baxter equation we find that the tree-level S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We show that the IRF form of the S-matrix meshes perfectly with the bootstrap equations.