The Structure of Non-Abelian Kinks

TL;DR

This paper analyzes non-abelian kink solutions in integrable 1+1D quantum field theories, exploring their boundary conditions, conserved charges, and consistency with proposed exact S-matrices, with relevance to AdS/CFT string models.

Contribution

It provides a detailed analysis of boundary conditions, charges, and the integrability structure of non-abelian kinks in generalized sine-Gordon theories.

Findings

Boundary conditions are complex due to WZ terms.

Kinks carry local and non-local conserved charges.

Their structure aligns with proposed exact S-matrices.

Abstract

We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that their structure is perfectly consistent with the exact factorizable S-matrices that have been proposed to describe these theories.