N = 2 super coulomb gas formalism

Abstract We study N = 2 super conformal field theories using a Coulomb gas formalism. We also discuss its applications to SU(2) Wess-Zumino-Witten models and Z k parafermionic theories. Using a BRST approach, we obtain the partition functions of Z k parafermions and related theories and give an explicit proof of the observations of Distler and Qiu. Some one-loop two-point functions of Z k parafermions are calculated. We also show that the coset models of the SU(2) WZW models can be obtained in an explicit operator form from the Feigin-Fuchs constructions.