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

TL;DR

This work provides a comprehensive, unified framework for generating and analyzing gravity duals of gauge theories with deformed products via TsT transformations. It connects star-product deformations (non-commutative, dipole, beta) to explicit TsT solution-generating procedures, deriving concrete NS-NS and RR backgrounds and detailing world-sheet and D-brane behaviors. Through two main examples—deformations of $\mathcal{N}=4$ SYM and the $\mathcal{N}=6$ ABJM theory—it shows how D-brane probes read out the modified moduli spaces, with rich vacuum structures emerging, especially for rational deformation parameters where brane polarization and orbifold branches occur. The results provide a robust toolkit for constructing and interpreting gravity duals of deformed gauge theories, highlighting how marginality, supersymmetry breaking, and non-locality emerge in the holographic context.

Abstract

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.