A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance

Abstract

We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N = 2 superconformal field theory (SCFT). We also establish interesting relations between N = 1 and N = 2 models of SCFT with central charges $(3/2)( 1 -{2(2 - 4\nu)^2}/{2(4\nu)})$ and $3(1 - 2/{4\nu})$. A number of new mock theta function identities are derived.