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arxiv: 1207.0413 · v1 · pith:3X3Y2FYWnew · submitted 2012-07-02 · ✦ hep-th · math-ph· math.MP

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

classification ✦ hep-th math-phmath.MP
keywords modelintegrabilitysigmatheorybosoniccasedeformationfermionic
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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.

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