N=4 Chern-Simons theories with auxiliary vector multiplets

TL;DR

The paper analyzes a class of 3D quiver Chern-Simons theories with some vanishing CS couplings, rendering certain vector multiplets auxiliary. By rewriting the action and supersymmetry transformations in manifest $Spin(4)$ covariant component form and carefully handling auxiliary fields, it demonstrates ${N}=4$ supersymmetry at the level of the CS-hyper sector. Integrating out the auxiliary fields drives the theory toward CS-matter dynamics with hyper-Kähler target spaces, and the construction is connected to a type IIB brane setup. This work extends prior ${N}=4$ CS theories by providing an explicit, covariant component-field realization and showing symmetry enhancement under the auxiliary-vector regime.

Abstract

We investigate a class of quiver-type Chern-Simons gauge theories with some Chern-Simons couplings vanishing. The vanishing of the couplings means that the corresponding vector fields are auxiliary fields. We show that these theories possess N=4 supersymmetry by writing down the actions and the supersymmetry transformation in terms of component fields in manifestly Spin(4) covariant form.