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

Determines from first principles the fusion rules of the logarithmic triplet model at central charge zero, finding a finite set of representations that closes under fusion. Applied to boundary conditions, it shows that, unlike in rational theories, only some representations give consistent boundary conditions.

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.

Recommended citation: M.R. Gaberdiel, I. Runkel and S. Wood, J. Phys. A 42, 325403 (2009)
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