On the integrability of two-dimensional models with U(1)xSU(N) symmetry

TL;DR

This paper investigates the integrability of models with U(1)xSU(N) symmetry, revealing that integrability is rare at higher N and proposing Bethe ansatz equations for the N=4 case related to string theory.

Contribution

It introduces a family of models with U(1)xSU(N) symmetry, analyzes their integrability properties, and proposes Bethe ansatz equations for the N=4 case connected to AdS/CFT correspondence.

Findings

Integrability is sporadic at higher N and requires fine-tuning.

The N=2 case is equivalent to a known integrable model.

Proposed Bethe ansatz equations for the N=4 model related to string theory.

Abstract

In this paper we study the integrability of a family of models with U(1)xSU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CP^(N-1) sigma model coupled to a self-interacting massless fermion, while the bosonic one defines a one-parameter deformation of the O(2N) sigma model. For N=2 the latter model is equivalent to the integrable deformation of the O(4) sigma model discovered by Wiegmann. At higher values of N we find that integrability is more sporadic and requires a fine-tuning of the parameters of the theory. A special case of our study is the N=4 model, which was found to describe the AdS_4xCP^3 string theory in the Alday-Maldacena decoupling limit. In this case we propose a set of asymptotic Bethe ansatz equations for the energy spectrum.