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

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

1995-07-12

arxiv.org/abs/hep-th/9507072v3

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, harvmac, no figures; new identities, proofs and comments added; misprints eliminated

Scientific paper

10.1007/BF02179546

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.

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