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

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.

61 pages, 7 figures

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Comments on operators with large spin
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
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Cited by in corpus (21)

• Jordanian deformations of the AdS_5xS^5 superstring
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• A Jordanian deformation of AdS space in type IIB supergravity
• Superisometries and integrability of superstrings
• Schrodinger Sigma Models and Jordanian Twists
• A deformation of quantum affine algebra in squashed WZNW models
• Exotic symmetry and monodromy equivalence in Schrodinger sigma models
• Bethe Ansaetze for GKP strings
• Integrable sigma models and 2-loop RG flow
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• The low energy limit of the AdS(3) x S(3) x M(4) spinning string
• String theories on warped AdS backgrounds and integrable deformations of spin chains
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• An Index for Quantum Integrability
• The classical and quantum particle on a flag manifold
• Integrable sigma models on Riemann surfaces
• ABJM flux-tube and scattering amplitudes
• Exact results for the low energy AdS(4)XCP(3) string theory
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Notes on index of quantum integrability