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

TL;DR

This paper develops a superspace background field method to analyze low-energy effective actions in three-dimensional extended SYM theories, revealing connections to M2 and D2 brane theories and classical Abelian models.

Contribution

It introduces a novel superspace approach to study effective actions in 3D SYM theories, linking them to brane dynamics and classical Abelian theories.

Findings

Effective action for N=2 quiver gauge theory matches classical Abelian ABJM theory.

Low-energy effective actions in pure N=2, N=4, N=8 SYM theories show correspondence with Abelian models.

The method confirms the M2 brane as an effective description of the D2 brane at strong coupling.

Abstract

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 studied. This gauge theory describes the D2 brane probing the conifold singularity. Surprisingly, the leading terms in this effective action reproduce the classical action of the Abelian ABJM theory confirming the fact that the M2 brane can be considered as the effective theory for the D2 brane at strong coupling. 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 the leading terms in its effective action and the classical action of the Abelian Gaiotto-Witten theory.