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

July 10, 2000

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.

Keywords:

*none*