S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

TL;DR

This paper explores the integrable structure of k-deformed sigma models, proposing exact S-matrices that reveal a hidden affine quantum group symmetry, supported by quantum inverse scattering evidence.

Contribution

It introduces a conjecture for the exact S-matrices of k-deformed sigma models, linking them to affine quantum group symmetry and providing initial evidence for this symmetry.

Findings

Proposed exact S-matrices for k-deformed sigma models.

Evidence of hidden affine quantum group symmetry.

Connection to quantum inverse scattering techniques.

Abstract

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with q=exp(i pi/k) a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.