On 4d rank-one N=3 superconformal field theories

TL;DR

This paper investigates 4d N=3 superconformal field theories with rank one, revealing their moduli space structure, supersymmetry enhancement, and associated exotic 2d chiral algebras, providing new insights into their mathematical properties.

Contribution

It classifies rank-one 4d N=3 SCFTs, determines their moduli space, supersymmetry enhancement conditions, and constructs their associated exotic 2d chiral algebras.

Findings

Moduli space is C^3/Z_k for k=1,2,3,4,6.

Supersymmetry enhances to N=4 for k=1,2.

Constructed exotic N=2 supersymmetric W-algebras.

Abstract

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.