Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings

TL;DR

This paper develops a general framework for non-abelian T-duality in Green-Schwarz strings, deriving transformation rules for backgrounds, and explores deformations via Yang-Baxter solutions that preserve integrability.

Contribution

It extends non-abelian T-duality to generic Green-Schwarz strings and introduces a method to generate integrable deformations using Yang-Baxter solutions.

Findings

Derived transformation rules for supergravity backgrounds under non-abelian T-duality.

Established a generalized Seiberg-Witten map for deformed backgrounds.

Showed that Yang-Baxter deformations preserve integrability in sigma models.

Abstract

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 Seiberg-Witten map. When applied to integrable sigma models these deformations preserve the integrability.