Bailey flows and Bose-Fermi identities for the conformal coset models $(A^{(1)}_1)_N\times (A^{(1)}_1)_{N'}/(A^{(1)}_1)_{N+N'}$

TL;DR

This paper demonstrates a Bailey flow from minimal models to certain coset models using higher-level Bailey lemmas, deriving Bose-Fermi identities and exploring their relation to renormalization group flows.

Contribution

It introduces a new Bailey flow connecting minimal models to coset models and derives Bose-Fermi identities for these models using fractional-level Cartan matrices.

Findings

Established Bailey flow from $M(p,p')$ to coset models

Derived Bose-Fermi identities for coset models

Discussed relations between Bailey flow and RG flow

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 $(A^{(1)}_1)_N\times (A^{(1)}_1)_{N'}/(A^{(1)}_1)_{N+N'}$ where $N$ is a positive integer and $N'$ 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 $M(p,p')$. Relations between Bailey and renormalization group flow are discussed.