Free field realizations for rank-one SCFTs

TL;DR

This paper constructs vertex operator algebras for all rank-one  superconformal field theories using free-field realizations, linking Higgs and Coulomb branch data to classify these theories.

Contribution

It provides a uniform free-field realization framework for rank-one  SCFTs, connecting low-energy moduli space data to vertex algebra structures.

Findings

Constructed vertex operator algebras for all rank-one  SCFTs.

Identified the role of Higgs and Coulomb data in constraining algebra structures.

Proposed a bottom-up classification scheme for low-rank SCFTs.

Abstract

In this paper, we construct the associated vertex operator algebras for all $\mathcal{N}=2$ superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly suitable framework for this task. The elementary building blocks of the construction are dictated by the low energy degrees of freedom on the Higgs branch, which are well understood for rank-one theories. We further analyze the interplay between Higgs and Coulomb data on the moduli space of vacua, which tightly constrain the overall structure of the free field realizations. Our results suggest a plausible bottom-up classification scheme for low-rank SCFTs incorporating vertex algebra techniques.