N=2 Supersymmetry and Bailey Pairs

TL;DR

This paper reveals a unifying Bailey pair framework that connects supersymmetric conformal field theories with non-supersymmetric models, providing new insights into their character calculations and renormalization flows.

Contribution

It introduces a Bailey pair-based approach to unify calculations of $N=1$ and $N=2$ supersymmetric conformal field theories with non-supersymmetric models, including derivations of models via Bailey flows.

Findings

Unified Bailey pair formulation for supersymmetric and non-supersymmetric models

Derived $M(p,p+1)$ from $M(p-1,p)$ using Bailey renormalization flow

Obtained $N=1$ and $N=2$ models with specific central charges

Abstract

We demonstrate that the Bailey pair formulation of Rogers-Ramanujan identities unifies the calculations of the characters of $N=1$ and $N=2$ supersymmetric conformal field theories with the counterpart theory with no supersymmetry. We illustrate this construction for the $M(3,4)$ (Ising) model where the Bailey pairs have been given by Slater. We then present the general unitary case. We demonstrate that the model $M(p,p+1)$ is derived from $M(p-1,p)$ by a Bailey renormalization flow and conclude by obtaining the $N=1$ model $SM(p,p+2)$ and the unitary $N=2$ model with central charge $c=3(1-2/p).$