Deformations of T 1,1 as Yang-Baxter sigma models

Abstract

We consider a family of deformations of T 1,1 in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T 1,1 , which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric. Next, we consider three-parameter deformations of T 1,1 by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case. It is worth noting that for AdS 5 × T 1,1 , classical integrability for the full sector has been argued to be lost. Hence our result indicates that the YangBaxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.

Chaotic strings in a near Penrose limit of AdS5 × T1,1

“…The coset in (2.4) can reproduce the metric correctly and even three-parameter deformations of T 1,1 [32] as shown in [33,34]. 3 Here the light-cone convention is slightly different from the one in [35][36][37].…”

Derivation of the action and symmetries of the q-deformed AdS5 × S 5 superstring

“…It is possible to extend this action to the case where the R-matrix involved is a solution of the classical Yang-Baxter equation (CYBE). Such an action was studied in [42][43][44][45][46]. It was shown in particular that the γ-deformation [47][48][49] falls within this class of deformations.…”

Lax pairs for deformed Minkowski spacetimes

“…Further remarkably, these deformations may work for non-integrable backgrounds, such as a Sasaki-Einstein manifold T 1,1 [33,34]. TsT transformations of T 1,1 [16,35] are reproduced as Yang-Baxter deformations [36,37]. Thus the connection between gravity solutions and classical r-matrices may deserve to be called the gravity/CYBE correspondence (For a short summary see [38]).…”