We build string backgrounds for Yang-Baxter deformations of the AdS4 × ℂℙ3 superstring generated by r-matrices satisfying the classical Yang-Baxter equation. We obtain the metric and the NSNS two-form of the gravity dual corresponding to noncommutative and dipole deformations of ABJM theory, as well as a deformed background with Schrödinger symmetry. The first two backgrounds may also be found by TsT transformations while for the last background we get a new family of non-relativistic ABJM theories with Schrödinger symmetry.

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.

We build the bosonic η-deformed AdS4 × $$ \mathbbm{CP} $$ CP 3 background generated by an r-matrix that satisfies the modified classical Yang-Baxter equation. In a special limit we find that it is the gravity dual of the noncommutative ABJM theory.

Lorentzian continuation of the Sine-Liouville model describes nonhomogeneous rolling closed string tachyon. Via T-duality, this relates to the gauged H 3 + Wess-Zumino-Witten model at subcritical level. This model is exactly solvable. We give a closed formula for the 3-point correlation functions for the model at level k within the range 0 < k < 2, which relates to the analogous quantity for k > 2 in a similar way as how the Harlow-Maltz-Witten 3-point function of timelike Liouville field theory relates to the analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov structure constants: we find that the ratio between both 3-point functions can be written in terms of quotients of Jacobi's θ-functions, while their product exhibits remarkable cancellations and eventually factorizes. Our formula is consistent with previous proposals made in the literature.

We consider the non-integrable bosonic backgrounds W2,4× T1,1 and AdS5× T1,1 and derive their bosonic η-deformed versions using an r-matrix that solves the modified Yang-Baxter equation obtaining new integrable deformed backgrounds.