Two dimensional fractional supersymmetric conformal field theories and the two point functions

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 $(L_{-1}, L_{0}, G_{-1/3})$and$(\bar{L}{-1}, \bar{L}{0}, \bar{G}_{-1/3})$, the two point functions of the component fields of supermultiplets are calculated.