On Kazama-Suzuki Duality between $\mathcal{W}_k(\mathfrak{sl}_4, f_{\rm sub})$ and $N=2$ Superconformal Vertex Algebra

TL;DR

This paper classifies instances of Kazama-Suzuki duality involving the $N=2$ superconformal algebra and a specific $ ext{W}$-algebra, establishing a new duality at central charge -15 and classifying related modules.

Contribution

It introduces a new Kazama-Suzuki duality between a subregular $ ext{W}$-algebra of $ ext{sl}_4$ and the $N=2$ superconformal algebra at $c=-15$, and classifies associated modules.

Findings

Established a new duality at $c=-15$

Classified irreducible modules for $ ext{W}_k( ext{sl}_4, f_{ m sub})$ at $k=-1$

Mapped duality conditions between $ ext{W}$-algebras and superconformal algebras

Abstract

We classify all possible occurrences of Kazama-Suzuki duality between the ${N=2}$ superconformal algebra $L^{N=2}_c$ and the subregular $\mathcal{W}$-algebra $\mathcal{W}_{k}(\mathfrak{sl}_4, f_{\rm sub})$. We establish a new Kazama-Suzuki duality between the subregular $\mathcal{W}$-algebra $\mathcal{W}_k(\mathfrak{sl}_4, f_{\rm sub})$ and the $N = 2$ superconformal algebra $L^{N=2}_{c}$ for $c=-15$. As a consequence of the duality, we classify the irreducible $\mathcal{W}_{k=-1}(\mathfrak{sl}_4, f_{\rm sub})$-modules.