Wind on the boundary for the Abelian sandpile model

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.

26 pages, 4 figures

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Cited by in corpus (15)

• Fusion rules and boundary conditions in the c=0 triplet model
• Abelian Sandpile Model on the Honeycomb Lattice
• Fusion Rules of the ${\mathcal{W}}_{p,q}$ Triplet Models
• Return probability for the loop-erased random walk and mean height in sandpile : a proof
• Logarithmic conformal invariance in the Abelian sandpile model
• Integrability and conformal data of the dimer model
• Boundary monomers in the dimer model
• Logarithmic two-point correlators in the Abelian sandpile model
• Refined conformal spectra in the dimer model
• Sandpile models in the large
• Finite-size corrections and scaling for the dimer model on the checkerboard lattice
• Three-leg correlations in the two component spanning tree on the upper half-plane
• Continuous Abelian Sandpile Model in Two Dimensional Lattice
• Sandpile probabilities on triangular and hexagonal lattices
• Spatial Asymmetric Two dimensional Continuous Abelian Sandpile Model