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

Abstract

We prove polynomial identities for the N=1 superconformal model SM(2,4ν) 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(2,4ν) and M(2ν-1,4ν). We also introduce a generalization of the Witten index which is expressible in terms of the Rogers false theta functions.

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

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Cited by in corpus (19)

• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• The Andrews-Gordon identities and $q$-multinomial coefficients
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• Supernomial coefficients, polynomial identities and $q$-series
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• On identities of the Rogers--Ramanujan type
• Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities
• T-Reflection
• $q$-Trinomial identities
• A Higher-Level Bailey Lemma: Proof and Application
• New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions
• SM(2,4k) fermionic characters and restricted jagged partitions
• On double sum generating functions in connection with some classical partition theorems
• Orientation Reversal and the Chern-Simons Natural Boundary
• Supersymmetric zeta functions and determinants
• Radial Limits of Partial Theta and Similar Series
• New polynomial analogues of Jacobi's triple product and Lebesgue's identities
• On simplifications of certain $q$-multisums
• Finite Rogers--Ramanujan type identities