Fusion Rules in N=1 Superconformal Minimal Models

TL;DR

This paper extends the Verlinde theorem to N=1 superconformal minimal models, providing a comprehensive method to determine fusion rules and fermionic parity, with applications to specific models and correlation functions.

Contribution

It generalizes the Verlinde theorem to N=1 superconformal models, including fermionic parity, and completes the Coulomb gas description of Ramond sector correlation functions.

Findings

Fusion rules derived from modular transformations match known models.

Results agree with superconformal Tricritical Ising and Ashkin-Teller models.

Enhanced Coulomb gas formulation for Ramond sector correlations.

Abstract

The generalization to N=1 superconformal minimal models of the relation between the modular transformation matrix and the fusion rules in rational conformal field theories, the Verlinde theorem, is shown to provide complete information about the fusion rules, including their fermionic parity. The results for the superconformal Tricritical Ising and Ashkin-Teller models agree with the known rational conformal formulation. The Coulomb gas description of correlation functions in the Ramond sector of N=1 minimal models is also discussed and a previous formulation is completed.