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Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings. (English) Zbl 1396.83045
Summary: We perform non-abelian T-duality for a generic Green-Schwarz string with respect to an isometry (super)group \(G\), and we derive the transformation rules for the supergravity background fields. Specializing to \(G\) bosonic, or \(G\) fermionic but abelian, our results reproduce those available in the literature. We discuss also continuous deformations of the T-dual models, obtained by adding a closed \(B\)-field before the dualization. This idea can also be used to generate deformations of the original (un-dualized) model, when the 2-cocycle identified from the closed \(B\) is invertible. The latter construction is the natural generalization of the so-called Yang-Baxter deformations, based on solutions of the classical Yang-Baxter equation on the Lie algebra of \(G\) and originally constructed for group manifolds and (super)coset sigma models. We find that the deformed metric and \(B\)-field are obtained through a generalization of the map between open and closed strings that was used also in the discussion by Seiberg and Witten of non-commutative field theories. When applied to integrable sigma models these deformations preserve the integrability.

MSC:
83E30 String and superstring theories in gravitational theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
16T25 Yang-Baxter equations
83C65 Methods of noncommutative geometry in general relativity
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