Determinant formulae and unitarity for the N = 2 superconformal algebras in two dimensions or exact results on string compactification

Abstract

Determinant formulae are presented for the periodic, antiperiodic and twisted N = 2 superconformal algebras in two dimensions, and a classification is derived of the unitary highest weight representations. Physical realisations of several of these representations are discussed. In particular, it is noted that the unitarity constraints apply to string compactification, giving results which are nonperturbative in the compactification radius.