N = 2 superconformal invariance in two-dimensional quantum field theories

Abstract

We construct N = 2 superconformal currents, vertex operators and four-point correlation functions using chiral superfields. The method generalizes works by Thorn and by Dotsenko and Fateev. In particular the discrete families of degenerate representations given in works by Di Vecchia et al. and Boucher et al. arise naturally, thereby constituting a derivation of the N = 2 superconformal dimensions of these representations. Finally, unitary representations of the N = 2 algebra in the twisted sector are constructed out of free fermions based on the model of Di Vecchia et al.