Low-energy effective actions in three-dimensional extended SYM theories

We develop the background field method in the N = 2, d = 3 superspace for studying effective actions in three-dimensional SYM models which live in the world-volume of various 2-branes. In particular, the low-energy effective action for the N = 2 quiver gauge theory with four chiral superfields in the bifundamental representation is calculated and studied. This gauge theory describes a D2 brane probing the conifold singularity. Surprisingly, the scale-invariant part of this effective action coincides with the classical action of the Abelian ABJM theory. Apart from this N = 2 quiver gauge theory we study the low-energy effective action in pure N = 2, N = 4 and N = 8 SYM theories with gauge group SU(N) spontaneously broken down to an Abelian subgroup. In particular, for the N = 4 SYM we find similar correspondence between its one-loop effective action and the classical action of the Abelian Gaiotto-Witten theory.