Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)

TL;DR

This paper establishes polynomial identities for the N=1 superconformal model SM(2,4 u), extending known character identities, and explores duality and index generalizations using advanced q-series techniques.

Contribution

It introduces new polynomial identities for SM(2,4 u), demonstrates a duality under q inversion, and generalizes the Witten index with connections to Rogers false theta functions.

Findings

Proved polynomial identities extending Fermi/Bose character identities.

Established a duality between SM(2,4 u) and M(2 u-1,4 u) models.

Generalized the Witten index using Rogers false theta functions.

Abstract

We prove polynomial identities for the N=1 superconformal model SM(2,4\nu) which generalize and extend the known Fermi/Bose character identities. Our proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations for q-series on the fermionic side. We use these polynomials to demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.