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, L0, G−1/(F+1)) and (L̄−1, L̄0, Ḡ−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. 1 e-mail:[email protected] 2e-mail:[email protected]