Two-Dimensional Fractional Supersymmetric Conformal Field Theories and the Two-Point Functions

Abstract

A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by (L−1, L0, G −1/3 ) and (L−1,L0,Ḡ −1/3 ), the two point functions of the component fields of supermultiplets are calculated.

On Linear Differential Equations Involving a Para-Grassmann Variable

“…Further applications have been in a parasupersymmetric extension of quantum mechanics [18,19,20,21,22], in particular in generalizations of the Pauli and Dirac equations [23,24] to describe particles with spin s > 1 2 , as well as in the closely related fractional supersymmetry [25,26,27,28,29]. Low dimensional field theories, in particular conformal field theories, have also been discussed [30,31,32,33,34,35,36,37,38,39] and a generalization of the Virasoro algebra has been discovered [40,41]. In particular in this approach the geometrical point of view of merging the ordinary variables with the para-Grassmann variables into a set of coordinates on a parasuperspace and considering the fractional supersymmetric fields as functions on this space has been used in close analogy to the well-known superspace and superfields.…”