Bailey flows and Bose-Fermi identities for the conformal coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$

Abstract

We use the recently established higher-level Bailey lemma and Bose-Fermi polynomial identities for the minimal models $M(p,p^{\prime })$ to demonstrate the existence of a Bailey flow from $M(p,p^{\prime })$ to the coset models $(A_1^{(1)}{)}_N\times (A_1^{(1)}{)}_{N^{\prime }}/(A_1^{(1)}{)}_{N+N^{\prime }}$ where $N$ is a positive integer and $N^{\prime }$ is fractional, and to obtain Bose-Fermi identities for these models. The fermionic side of these identities is expressed in terms of the fractional-level Cartan matrix introduced in the study of $M(p,p^{\prime })$. Relations between Bailey and renormalization group flow are discussed.

28 pages, AMS-Latex, two references added

References in corpus (1)

• Supernomial coefficients, polynomial identities and $q$-series

Cited by in corpus (8)

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• Fused RSOS Lattice Models as Higher-Level Nonunitary Minimal Cosets
• Non-unitary minimal models, Bailey's lemma and N=1,2 superconformal algebras
• Staggered and affine Kac modules over $A_1^{(1)}$
• On simplifications of certain $q$-multisums