Bailey flows and Bose-Fermi identities for the conformal coset models ( A1(1)) N × ( A1(1)) N′ /( A1(1)) N+ N′

Abstract

We use the recently established higher-level Bailey lemma and Bose-Fermi polynomial identities for the minimal models M( p, p′) to demonstrate the existence of a Bailey flow from M( p, p′ ) to the coset models ( A 1 (1)) N × ( A 1 (1)) N′ /( A 1 (1)) N+ N′ where N is a positive integer and N′ is fractional, and to obtain Bose-Fetmi 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′). Possible relations between Bailey and renormalization group flow are discussed.