THE STRUCTURE OF OFFSHELL 3D SUPERSPACE WITH ARBITRARY N, COUPLED TO A YANG MILLS FIELD
THE STRUCTURE OF OFFSHELL 3D SUPERSPACE WITH ARBITRARY N, COUPLED TO A YANG MILLS FIELD
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Date
2010
Authors
Chapman, Daniel Molson
Advisor
Gates, Sylvester J
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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