String Backgrounds of the Yang-Baxter Deformed $AdS_4\times\mathbb{CP}^3$ Superstring

We build string backgrounds for Yang-Baxter deformations of the $AdS_4\times\mathbb{CP}^3$ superstring generated by $r$-matrices satisfying the classical Yang-Baxter equation. We obtain the metric and the NS-NS two-form of the gravity dual corresponding to noncommutative and dipole deformations of ABJM theory, as well as a deformed background with Schr\"odinger 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 Schr\"odinger symmetry.