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Yang-Baxter Deformations of the $AdS_5\times T^{1,1}$ Superstring and their Backgrounds

We consider three-parameter Yang-Baxter deformations of the $AdS_5\times T^{1,1}$ superstring for abelian $r$-matrices which are solutions of the classical Yang-Baxter equation. We find 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