A Jordanian deformation of AdS space in type IIB supergravity

Abstract

We consider a Jordanian deformation of the AdS5×S5 superstring action by taking a simple R-operator which satisfies the classical Yang-Baxter equation. The metric and NS-NS two-form are explicitly derived with a coordinate system. Only the AdS part is deformed and the resulting geometry contains the 3D Schrödinger spacetime as a subspace. Then we present the full solution in type IIB supergravity by determining the other field components. In particular, the dilaton is constant and a R-R three-form field strength is turned on. The symmetry of the solution is [SL(2, $$ \mathbb{R} $$ ) × U(1)2] × [SU(3) × U(1)] and contains an anisotropic scale symmetry.