Classification of GRW boundary conditions

Classify all GRW boundary theories, equivalently all symmetric Frobenius algebras in the ribbon Grothendieck–Verdier category of modules over the triplet vertex operator algebra W2,3 at central charge zero.

Background

The paper shows that GRW boundary theories for the triplet W2,3 at c=0 are exactly symmetric Frobenius algebras in its ribbon Grothendieck–Verdier module category. It also proves that every such boundary theory produces a consistent system of singular correlators.

Although the chiral symmetry algebra W(0) supplies an example, the complete classification of GRW boundary conditions remains unresolved. Such a classification would enumerate the possible boundary theories and the corresponding singular correlator systems.