Fusion algebra of critical percolation

Rasmussen, Jorgen and Pearce, Paul A. (2007) Fusion algebra of critical percolation. Journal of Statistical Mechanics: Theory and Experiment, 2007 P09002.1-P09002.15. doi:10.1088/1742-5468/2007/09/P09002

Author Rasmussen, Jorgen
Pearce, Paul A.
Title Fusion algebra of critical percolation
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2007-09
Sub-type Article (original research)
DOI 10.1088/1742-5468/2007/09/P09002
Volume 2007
Start page P09002.1
End page P09002.15
Total pages 15
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations that we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite direct sum of these representations. The fusion rules are commutative, associative and exhibit an sl (2) structure. They involve representations which we call Kac representations of which some are reducible yet indecomposable representations of rank 1. In particular, the identity of the fusion algebra is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the recent results of Eberle-Flohr and Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of indecomposable representations of rank 3. Our fusion rules are supported by extensive numerical studies of an integrable lattice model of critical percolation. Details of our lattice findings and numerical results will be presented elsewhere.
Keyword Conformal field theory
Percolation problems (theory)
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # P09002

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 21 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 14 Mar 2012, 14:18:31 EST by Kay Mackie on behalf of Mathematics