Fusion rules and boundary conditions in thec= 0 triplet model

Matthias R Gaberdiel, Ingo Runkel, Simon Wood
2009 Journal of Physics A: Mathematical and Theoretical  
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
more » ... e 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.
doi:10.1088/1751-8113/42/32/325403 fatcat:xy3tflodz5dnbn2xpiqtzvnkpm