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

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arxiv 1207.0413 v1 pith:3X3Y2FYW submitted 2012-07-02 hep-th math-phmath.MP

classification hep-thmath-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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  1. On the space of U(N) scattering amplitudes

    hep-th 2025-04 conditional novelty 6.0 of 10

    New rigorous bounds chart the allowed space of U(N) symmetric 2D scattering amplitudes, with a previously overlooked integrable solution (class VII) at the boundary and periodic extremal amplitudes.

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