Local β-deformations and Yang-Baxter sigma model

Abstract

Homogeneous Yang-Baxter (YB) deformation of AdS₅ × S⁵ 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 β-deformations of the AdS₅ ×S⁵ 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 β-deformations of H-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.