  We present a method for classifying conformal field theories based on Coulomb
gases (bosonic free-field construction). Given a particular geometric
configuration of the screening charges, we give necessary conditions for the
existence of degenerate representations and for the closure of the
vertex-operator algebra. The resulting classification contains, but is more
general than, the standard one based on classical Lie algebras. We then apply
the method to the Coulomb gas theory for the two-flavoured loop model of
Jacobsen and Kondev. The purpose of the study is to clarify the relation
between Coulomb gas models and conformal field theories with extended
symmetries.
