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

Abstract

The logarithmic triplet model W2,3 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 W2,3 theory. Unlike the familiar Cardy case where there is a consistent boundary condition for every representation of the chiral algebra, we find that for W2,3 only a subset of representations gives rise to consistent boundary conditions. These then have boundary spectra with non-degenerate two-point correlators.