On the integrability of two-dimensional models with image symmetry Original Research Article

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