Supercoset construction of Yang–Baxter-deformed AdS5×S5 backgrounds

Abstract

We study Yang–Baxter deformations of the AdS5×S5 superstring with the classical Yang–Baxter equation. We make a general argument on the supercoset construction and present a formula to describe the dilaton in terms of classical r-matrices. The supercoset construction is explicitly performed for some classical r-matrices, and the full backgrounds including the Ramond–Ramond (R–R) sector and dilaton are derived. Within the class of Abelian r-matrices, perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, γ-deformations of S5 and Schrödinger spacetimes. It is remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric. In particular, three-parameter γ-deformations of S5 and Schrödinger spacetimes do not preserve any supersymmetries. As for non-Abelian r-matrices, we will focus upon a specific example. The resulting background does not satisfy the equation of motion of the Neveu–Schwarz–Neveu–Schwarz two-form because the R–R three-form is not closed.