Fusion rules for the continuum sectors of the Virasoro algebra with c=1

TL;DR

This paper investigates the fusion rules of continuum sectors in the Virasoro algebra with central charge c=1, revealing how these sectors relate to SU(2) current algebra representations and introducing a new method for sector determination.

Contribution

It introduces a novel approach to analyze continuum sectors of the Virasoro algebra at c=1 and computes fusion rules involving these sectors and discrete ones.

Findings

Fusion rules for continuum and discrete sectors are explicitly computed.

A new method for determining the sector of a state is proposed.

Continuum sectors are characterized via localized homomorphisms into the current algebra.

Abstract

The Virasoro algebra with c=1 has a continuum of superselection sectors characterized by the ground state energy h. Only a discrete subset of sectors arises by restriction of representations of the SU(2) current algebra at level k=1. The remaining continuum of sectors is obtained with the help of (localized) homomorphisms into the current algebra. The fusion product of continuum sectors with discrete sectors is computed. A new method of determining the sector of a state is used.