Wind on the boundary for the Abelian sandpile model
(2007) Journal of Statistical Mechanics: Theory and Experiment — Vol. 2007, n° 09, p. P09013-P09013 (2007)
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- Abstract
- We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge $c=-2$, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights $-1/8,\,0$ and $3/8$), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.
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Ruelle, P. (2007). Wind on the boundary for the Abelian sandpile model. Journal of Statistical Mechanics: Theory and Experiment, 2007(09), P09013-P09013. https://doi.org/10.1088/1742-5468/2007/09/P09013 (Original work published 2007)