THE STRUCTURE OF OFFSHELL 3D SUPERSPACE WITH ARBITRARY N, COUPLED TO A YANG MILLS FIELD

Abstract

We introduce the form of 3D Superspace as a Z2-graded Lie Algebra. A set

of Superspace Algebras can be defined in this way, characterized by the number of

supercharges, N. Superspace will then be coupled to a Yang Mills field, to create

a covariant derivative algebra. Various constraints must then be implemented, for

consistency and in order to form an irreducible representation of this algebra. An

in-depth view into the well-known example of N = 2 will be given, as well as a

comparison with the corresponding compactification of 4D N=1. Then, the theory

will be expanded to N = 3 and N = 4, before attempting to generalize to arbitrary N.

However, beyond N = 4, the theory is discovered to only be known to be consistent

at N = 8. The corresponding 2-point superfield and component actions are shown,

as a basis for later theories