F-theorem, duality and SUSY breaking in one-adjoint Chern–Simons–Matter theories

We extend previous work on N=2N=2 Chern–Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q  -deformed S3S3 partition functions. An explicit illustration based on the known analytic solution of the Chern–Simons matrix model is presented.