Fusion rules and boundary conditions in the c=0 triplet model

Understand

The logarithmic triplet model W_2,3 at c=0 is studied.

• In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all irreducible representations, that closes under fusion.
• With the help of these results we then investigate the possible boundary conditions of the W_2,3 theory.
• Unlike the familiar Cardy case where there is a consistent boundary condition for every representation of the chiral algebra, we find that for W_2,3 only a subset of representations gives rise to consistent boundary conditions.