A Study of Equivalence of SUSY Theories using Adinkras and Super Virasoro Algebras
Chappell, Isaac Samuel
Gates, Sylvester J
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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  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 ,) we show that one is contained inside the other which allows some new OPEs to be calculated.