The theory of physical superselection sectors in terms of vertex operator algebra language

TL;DR

This paper interprets the theory of physical superselection sectors using vertex operator algebra language, constructing simple currents and algebra extensions, with applications to affine Lie algebra-related VOAs.

Contribution

It introduces a vertex operator algebra framework for superselection sectors, constructing simple currents and algebra extensions, and applies these to affine Lie algebra VOAs.

Findings

Constructed simple currents from primary semisimple elements of weight one.

Proved conditions under which VOA extensions by simple currents are rational.

Presented two equivalent methods for twisted module constructions.

Abstract

We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a primary semisimple element of weight one. We then prove that if a rational vertex operator algebra $V$ has a simple current $M$ satisfying certain conditions, then $V\oplus M$ has a natural rational vertex operator (super)algebra structure. Applying our results to a vertex operator algebra associated to an affine Lie algebra, we construct its simple currents and the extension by a simple current. We also present two essentially equivalent constructions for twisted modules for an inner automorphism from the adjoint module or any untwisted module.