Central charge and the Andrews-Bailey construction

From the equivalence of the bosonic and fermionic representations of finiti zed characters in conformal field theory, one can extract mathematical obje cts known as Bailey pairs. Recently Berkovich, McCoy, and Schilling have co nstructed a "generalized" character formula depending on two parameters rho (1) and rho(2), using the Bailey pairs of the unitary model M(p-1,p). By ta king appropriate limits of these parameters, they were able to obtain the c haracters of model M(p,p+1), N = 1 model SM(p,p+2), and the unitary N=2 mod el with central charge c = 3(1-2/p). In this letter we computed the effecti ve central charge associated with this "generalized" character formula usin g a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models. (C) 1999 American Institute of Physics. [S0022-2488(99)02307-5].