N=8 Superspace Constraints for Three-dimensional Gauge Theories

TL;DR

This paper systematically analyzes N=8 superspace constraints in three dimensions, unifying the description of super Yang-Mills and BLG models through an SO(8) tensor framework.

Contribution

It introduces a universal SO(8) tensor formalism that encodes couplings of vector and scalar supermultiplets in three-dimensional N=8 superspace.

Findings

Unified formulation of BLG and super Yang-Mills models

Explicit SO(8) tensor W_{AB} satisfying superspace constraints

Framework applicable to various three-dimensional supersymmetric theories

Abstract

We present a systematic analysis of the N=8 superspace constraints in three space-time dimensions. The general coupling between vector and scalar supermultiplets is encoded in an SO(8) tensor W_{AB} which is a function of the matter fields and subject to a set of algebraic and super-differential relations. We show how the conformal BLG model as well as three-dimensional super Yang-Mills theory provide solutions to these constraints and can both be formulated in this universal framework.