A Study of Equivalence of SUSY Theories using Adinkras and Super Virasoro Algebras
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Abstract
Supersymmetry (SUSY) theories describe a wide number of quantum
field theories with supersymmetric particles interacting. By using two
methods, Adinkras and Super Virasoro algebras (SVAs), more
information is gained about SUSY theories: (a.) when two
representation may be considered equivalent, that is, describing
the same physics, and (b.) the derivation of OPE's that do not rely on
Wick rotations. Adinkras [1] are objects that encode important
information about the theory in graphs. These graphs can be translated
into matrices through what is now called a Garden Algebra. In a specfiic
example, (d=4, N=4 SUSY theories,) it is found that there are six
classes of SUSY theories through studying the Adinkras by one
definition. However, using a criterion that is motivated by physical
considerations of four dimensional field theories, this number is
reduced to only three. Super Virasoro Algebras are close relatives of
Super Conformal Algebras that contain a Lie algebra. They can be used
to find Operator Product Expansions which are related to two-point
correlation functions. By comparison of two different realizations of SVAs
(the Geometrically Realization GR and the one developed by Hasiewicz,
Thielemans, Troost [2],) we show that one is contained inside the other
which allows some new OPEs to be calculated.