On deformed gauge theories and their string/M-theory duals

We present general formulae for the TsT transformation (T-duality, shift, T-duality) of type II string backgrounds and open string boundary conditions. The TsT transformation provides a systematic procedure to find string theory duals of gauge theories with deformed products of fields in the lagrangian, and the duals can be analyzed by using transformed D-brane probes. As examples illustrating some features of the deformed theories, we consider the known backgrounds dual to non-commutative, dipole and beta-deformed N=4 Super Yang-Mills as well as new backgrounds dual to deformations of the recently proposed N=6 Chern-Simons-matter theory living on multiple M2-branes on an orbifold.