Generators of a Bosonic VOA and Connections to a Boundary VOA

TL;DR

This paper identifies generators of specific bosonic vertex operator algebras (VOAs) related to certain SU(n) theories and explores their algebraic structure and boundary connections.

Contribution

It provides a method to identify generators of bosonic VOAs associated with particular SU(n) theories and conjectures their algebraic construction.

Findings

Generators for bosonic VOAs are explicitly identified.

The algebraic structure of these VOAs can be constructed from the identified generators.

Boundary VOAs naturally include the bosonic VOAs.

Abstract

We show how to identify generators of bosonic VOAs associated with $T_{[n-1,1]}^{[1^n]}(SU(n))$ and $T_{[n-1,1^2]}^{[2,1^{n-1}]}(SU(n+1))$, and conjecture that the algebraic structure of these VOAs can be constructed by these generators. We also find out that the boundary VOA associated with $T_{[n-1,1]}^{[1^n]}(SU(n))$ naturally includes the bosonic VOA.