Yang-Baxter deformations of the AdS5 × T1,1 superstring and their backgrounds

Abstract

We consider three-parameter Yang-Baxter deformations of the AdS5× T1,1 superstring for abelian r-matrices which are solutions of the classical Yang-Baxter equation. We find the NSNS fields of two new backgrounds which are dual to the dipole deformed Klebanov-Witten gauge theory and to the nonrelativistic Klebanov-Witten gauge theory with Schrödinger symmetry.

Chaotic string dynamics in deformed T1,1

“…has been discussed in [15]. Yang-Baxter deformations [16][17][18][19][20][21] of T 1,1 are discussed in [15,22,23] (For a short summary, see [24]).…”

Integrable deformed T1,1 sigma models from 4D Chern-Simons theory

“…is also one of the non-integrable examples [40][41][42]. For the coset construction of T 1,1 and its Yang-Baxter deformation, see [43,44]. The AdS 5 × T 1,1 geometry is well studied because it is a gravity dual of N = 1 superconformal field theory (SCFT) [45].…”

Bosonic $η$-deformations of Non-integrable Backgrounds

“…This would enlarge the power of this tool to obtain integrable models. First results were given for the AdS 5 × T 1,1 [20,21] and W 2,4 × T 1,1 [22] backgrounds. In particular, W 2,4 × T 1,1 gives rise to a somewhat exotic background that has been explored in [23,24] 2 , which is non-integrable, since W 2,4 can be realized as the double Wick rotation of T 1,1 , which exhibits a chaotic behavior and then is non-integrable [26].…”

“…But, since chaotic behavior was found in T 1,1 , we could expect it also in W 2,4 and then the σ-model on (2.1) should be non-integrable. Notice that this coset has extra factors of SO(2) r × U (1) R in the numerator and two U (1)'s in the denominator in order to take into account all isometries of the space [20,21] The Lie algebra that generates this space can then be written as…”

“…Thus, in order to compute the deformed background with Lagrangian (3.1) we need first to compute the the non-zero components Λ n m in (3.2) and then follow the same procedure as in [19,21]. We find that…”