sl^(2)_{-1/2}: A Case Study

Abstract

The construction of the non-logarithmic conformal field theory based on sl^(2)_{-1/2} is revisited. Without resorting to free-field methods, the determination of the spectrum and fusion rules is streamlined and the beta gamma ghost system is carefully derived as the extended algebra generated by the unique finite-order simple current. A brief discussion of modular invariance is given and the Verlinde formula is explicitly verified.