Local $\beta$-deformations and Yang-Baxter sigma model

TL;DR

This paper explores the relationship between homogeneous Yang-Baxter deformations and $eta$-deformations of AdS$_5 imes$ S$^5$, providing a formalism that connects these deformations with superstring actions and supergravity solutions.

Contribution

It demonstrates the equivalence of homogeneous YB deformations to $eta$-deformations for bosonic classical r-matrices and formulates a string action invariant under O(10,10) symmetry up to quadratic fermions.

Findings

Homogeneous YB deformations correspond to $eta$-deformations with bosonic r-matrices.

An O(10,10)-invariant string action reproduces superstring dynamics up to quadratic fermions.

Solutions of generalized supergravity are obtained for $H$-fluxed AdS backgrounds.

Abstract

Homogeneous Yang-Baxter (YB) deformation of AdS$_5\times$S$^5$ superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to $\beta$-deformations of the AdS$_5\times$S$^5$ background when the classical $r$-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10,10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing $H$-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study $\beta$-deformations of $H$-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.