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 $(L_{-1},L_{0},G_{-1/(F+1)})$ and $(\bar{L}_{-1},\bar{L}_{0},\bar{G}_{-1/(F+1)})$, 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. 
Fardin Kheirandish and Mohammad Khorrami