A trinomial analogue of Bailey’s lemma and \(N=2\) superconformal invariance. (English) Zbl 0906.05004

Summary: 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 \({3\over 2}\left(1-{2(2-4\nu)^2\over 2(4\nu)}\right)\) and \(3\left(1- {2\over 4\nu}\right)\). A number of new mock theta function identities are derived.


05A19 Combinatorial identities, bijective combinatorics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
11P82 Analytic theory of partitions
05A30 \(q\)-calculus and related topics
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