Mass-Deformed Super Yang-Mills Theories from M2-Branes with Flux

Abstract

We consider $(2+1)$-dimensional mass-deformed SYM theories and their M-theory origin. These are obtained from MP Higgsing of ABJM theory with constant flux and fixing the mass terms via supersymmetry completion. Depending on the choice of the flux, we obtain ${\cal N}=1$, ${\cal N}=2$, and ${\cal N}=4$ mass-deformed SYM theories. For each of these cases we solve the vacuum equation and obtain the fuzzy two sphere solution for the first two cases. We also discuss the D-brane interpretation of the obtained mass-deformed SYM theories.