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

Abstract

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. These then have boundary spectra with non-degenerate two-point correlators.

50 pages; v2: changed formulation in section 1.2.1 and corrected typos, version to appear in J. Phys. A

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