# Free Field Realizations from the Higgs Branch

## TL;DR

This paper constructs free field realizations of vertex operator algebras associated with 4D $
abla=2$ superconformal theories, linking Higgs branch geometry to algebraic structures using minimal chiral bosons and additional ingredients.

## Contribution

It introduces a novel method to realize associated VOAs from Higgs branch data with minimal free fields, including cases with extra degrees of freedom.

## Key findings

- Realizations use a small set of chiral bosons matching Higgs branch dimension.
- Incorporates symplectic fermions for vector multiplets.
- Provides a natural R-filtration of the associated VOA.

## Abstract

We present free field realizations for the associated vertex operator algebras of a number of four-dimensional $\mathcal{N}=2$ superconformal field theories. Our constructions utilize an exceptionally small set of chiral bosons whose number matches the complex dimensionality of the Higgs branch of the superconformal field theory. In the case of theories whose Higgs branches support additional degrees of freedom (free vector multiplets or decoupled interacting SCFTs), the corresponding "free field realizations" include additional ingredients: symplectic fermions in the case of vector multiplets and a $C_2$ co-finite VOA in the case of a residual interacting SCFT. The resulting picture is that the associated VOA can be constructed from the Higgs branch effective theory via free field realization. Our constructions also provide a natural realization of the $R$-filtration of the associated VOA.