Unitarity of minimal $W$-algebras and their representations II: Ramond sector

TL;DR

This paper classifies unitary Ramond twisted representations of minimal W-algebras, computes their characters, and derives denominator identities, advancing understanding of superconformal algebra representations.

Contribution

It provides a classification of irreducible highest weight Ramond twisted representations and computes their characters, with some results based on conjectures about the quantum Hamiltonian reduction.

Findings

Classified all irreducible Ramond twisted representations with non-Ramond extremal highest weight.

Computed characters and derived denominator identities for superconformal algebras.

Identified open problems in unitarity for Ramond extremal cases.

Abstract

In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well as in the untwisted extremal case, remains open). We compute the characters of these representations and deduce from them the denominator identities for all superconformal algebras in the Neveu-Schwarz and Ramond sector. Some of the results rely on conjectures about the properties of the quantum Hamiltonian reduction functor in the Ramond sector.