Unitarity of rational N=2 superconformal theories

TL;DR

This paper proves that all rational N=2 superconformal models are unitary, using algebraic, modular, and coset methods, and suggests this might extend to all such models.

Contribution

It provides a comprehensive proof of unitarity for rational N=2 super Virasoro models using multiple approaches, including Zhu's algebra and coset constructions.

Findings

All rational N=2 super Virasoro models are unitary.

Explicit determination of Zhu's algebra for certain theories.

Modular analysis supports unitarity of these models.

Abstract

We demonstrate that all rational models of the N=2 super Virasoro algebra are unitary. Our arguments are based on three different methods: we determine Zhu's algebra (for which we give a physically motivated derivation) explicitly for certain theories, we analyse the modular properties of some of the vacuum characters, and we use the coset realisation of the algebra in terms of su_2 and two free fermions. Some of our arguments generalise to the Kazama-Suzuki models indicating that all rational N=2 supersymmetric models might be unitary.