Wind on the boundary for the Abelian sandpile model

Details Wind on the boundary for the Abelian sandpile model Wind on the boundary for the Abelian sandpile model

2007-07-25

arxiv.org/abs/0707.3766v2

J. Stat. Mech. (2007) P09013

Physics

Condensed Matter

Statistical Mechanics

26 pages, 4 figures

Scientific paper

10.1088/1742-5468/2007/09/P09013

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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