  Two-dimensional full conformal field theories have been studied in various
mathematical frameworks, from algebraic, operator-algebraic to categorical. In
this work, we focus our attention on theories with chiral components having
pointed braided tensor representation subcategories, namely having
automorphisms whose equivalence classes necessarily form an abelian group. For
such theories, we exhibit the explicit Hilbert space structure and construct
primary fields as Wightman fields for the two-dimensional full theory. Given a
finite collection of chiral components with automorphism categories with
trivial total braiding, we also construct a local extension of their tensor
product as a chiral component. We clarify the relations with the Longo-Rehren
construction, and illustrate these results with concrete examples including the
U(1)-current.
