TL;DR
This paper revisits the non-logarithmic conformal field theory based on sl^(2)_{-1/2}, providing a streamlined approach to spectrum, fusion rules, and modular invariance without free-field methods.
Contribution
It offers a new, simplified derivation of the spectrum and fusion rules for the sl^(2)_{-1/2} theory, including the explicit verification of the Verlinde formula.
Findings
Derived the spectrum and fusion rules without free-field methods
Explicitly verified the Verlinde formula for the theory
Analyzed the modular invariance properties
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.
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