Two-dimensional fractional supersymmetric conformal- and logarithmic 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. Applying the generators of the closed subalgebra generated by $(L_{-1},L_0,G_{-1\mathrm{/}(F+1)})$ and $({\bar{L}}_{-1},{\bar{L}}_0,{\bar{G}}_{-1\mathrm{/}(F+1)})$, the two point functions of the component-fields of supermultiplets are calculated. Then the logarithmic superconformal field theories are investigated and the chiral and full two-point functions are obtained.