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Non-chiral current algebras for deformed supergroup WZW models

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Abstract

We study deformed WZW models on supergroups with vanishingKilling form. The deformation is generated by the isotropic current-current perturbation which is exactly marginal under these assumptions. It breaks half of the global isometries of the original supergroup. The current corresponding to the remaining symmetry is conserved but its components are neither holomorphic nor anti-holomorphic. We obtain the exact two-and three-point functions of this current and a four-point function in the first two leading orders of a 1/k expansion but to all orders in the deformation parameter. We further study the operator product algebra of the currents, the equal time commutators and the quantum equations of motion. The form of the equations of motion suggests the existence of non-local charges which generate a Yangian. Possible applications to string theory on Anti-de Sitter spaces and to condensed matter problems are briefly discussed.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, United Kingdom

    Anatoly Konechny

  2. Maxwell Institute for Mathematical Sciences, Edinburgh, United Kingdom

    Anatoly Konechny

  3. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937, Cologne, Germany

    Thomas Quella

  4. Korteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, PO Box 94248, 1090, GE, Amsterdam, The Netherlands

    Thomas Quella

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  1. Anatoly Konechny
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Correspondence to Anatoly Konechny.

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ArXiv ePrint: 1011.4813

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Konechny, A., Quella, T. Non-chiral current algebras for deformed supergroup WZW models. J. High Energ. Phys. 2011, 124 (2011). https://doi.org/10.1007/JHEP03(2011)124

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