A Jordanian deformation of AdS space in type IIB supergravity

Abstract

We consider a Jordanian deformation of the AdS_5xS^5 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 Schrodinger 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,R)xU(1)^2] x [SU(3)xU(1)] and contains an anisotropic scale symmetry.Comment: 29 pages, no figure, LaTeX, typos corrected, references added, further clarification adde

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

“…Finally, we should comment on a possible relation between the q-deformed AdS 5 ×S 5 and a Jordanian deformation of AdS 5 ×S 5 argued in [54]. The null-like warped SL(2) LLSM is obtained as a pp-wave like limit of the time-like warped one, as explained in appendix D. The identical null-like warped SL(2) LLSM is also derived from a string sigma model on Sch 3 ×S 1 .…”

“…Indeed, this is the case. As explained in detail in [53] , the r-matrix that leads to the Jordanian deformed solution [54] is constructed by performing a Jordanian twist of the r-matrix of Drinfeld-Jimbo type [45,46]. Hence this observation suggests that the Jordanian twist at the r-matrix level corresponds to the pp-wave like limit at the geometry level, as depicted in figure 1.…”

“…This system is derived as a pp-wave like limit of the time-like warped SL(2) LLSM, as shown in detail in appendix D. The resulting system also coincides with a fast-moving string limit of Sch 3 ×S 1 subsector of the Jordanian deformed AdS 5 ×S 5 superstring action [53,54]. It is convenient to introduce a vector notation n a ,…”

“…The null-like warped SL(2) LLSM is obtained as a pp-wave like limit of the time-like warped one, as explained in appendix D. The identical null-like warped SL(2) LLSM is also derived from a string sigma model on Sch 3 ×S 1 . Then the geometry of Sch 3 ×S 1 is contained as a subspace of a Jordanian deformed AdS 5 ×S 5 [54].…”

“…A remarkable point is that partial deformations are possible in comparison to the standard q-deformation. In fact, as an example of deformation of AdS 5 , a complete type IIB supergravity solution has been found in [54] and it contains a three-dimensional Schrödinger spacetime (Sch 3 ) as a JHEP08 (2014)110 subspace. Furthermore, γ-deformed backgrounds [55,56] and the gravity duals for noncommutative gauge theories [57][58][59] have been reproduced in [60] and [61], respectively, in the context of the Yang-Baxter sigma model.…”