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Abstract: We continue our investigation of the two-dimensional Abelian sandpile modelin terms of a logarithmic conformal field theory with central charge c=-2, byintroducing two new boundary conditions. These have two unusual features: theycarry an intrinsic orientation, and, more strangely, they cannot be imposeduniformly on a whole boundary like the edge of a cylinder. They lead to sevennew boundary condition changing fields, some of them being in highest weightrepresentations weights -1-8, 0 and 3-8, some others belonging toindecomposable representations with rank 2 Jordan cells lowest weights 0 and1. Their fusion algebra appears to be in full agreement with the fusion rulesconjectured by Gaberdiel and Kausch.



Author: Philippe Ruelle

Source: https://arxiv.org/







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