A Study of Equivalence of SUSY Theories using Adinkras and Super Virasoro Algebras

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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 [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.