Deformation quantizations from vertex operator algebras

TL;DR

This paper explores how vertex operator algebras from 4D N=2 superconformal theories encode the deformation quantization of the Higgs branch in the reduced 3D theory, depending on symmetry mixing.

Contribution

It establishes conditions under which the vertex operator algebra recovers the Higgs branch deformation quantization, highlighting the role of R-symmetry mixing during RG flow.

Findings

Positive recovery of deformation quantization when R-symmetries do not mix.

Identification of altered quantization parameters when R-symmetries mix.

Extension of the correspondence to cases with symmetry mixing.

Abstract

In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. We answer this question positively if the UV R-symmetries do not mix with accidental (topological) symmetries along the renormalization group flow from the four-dimensional theory on a circle to the three-dimensional theory. If they do mix, we still find a deformation quantization but at different values of its period.