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 $(3/2)( 1 -{2(2 - 4ν)^2}/{2(4ν)})$ and $3(1 - 2/{4ν})$. A number of new mock theta function identities are derived.