Central Charge and the Andrews-Bailey Construction

TL;DR

This paper computes the effective central charge from a generalized character formula in conformal field theory, revealing a simple dilogarithm expression that interpolates between known unitary model central charges.

Contribution

It introduces a method to calculate the effective central charge from a generalized character formula using saddle point analysis, connecting various unitary models.

Findings

Derived a dilogarithm expression for the effective central charge.

Interpolates between central charges of different unitary models.

Provides a unified framework for understanding model relationships.

Abstract

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have constructed a `generalized' character formula depending on two parameters $\ra$ and $\r2$, using the Bailey pairs of the unitary model $M(p-1,p)$. By taking appropriate limits of these parameters, they were able to obtain the characters of model $M(p,p+1)$, $N=1$ model $SM(p,p+2)$, and the unitary $N=2$ model with central charge $c=3(1-{\frac{2}{p}})$. In this letter we computed the effective central charge associated with this `generalized' character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.