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

In this paper we study the integrability of a family of models with U(1)×SU(N)U(1)×SU(N) symmetry. They admit fermionic and bosonic formulations related through bosonization and subsequent T-duality. The fermionic theory is just the CPN−1CPN−1 sigma model coupled to a self-interacting massless fermion, while the bosonic one defines a one-parameter deformation of the O(2N)O(2N) sigma model. For N=2N=2 the latter model is equivalent to the integrable deformation of the O(4)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=4N=4 model, which was found to describe the AdS4×CP3AdS4×CP3 string theory in the Alday–Maldacena decoupling limit. In this case we propose a set of asymptotic Bethe ansatz equations for the energy spectrum.