Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-08-26
Nucl.Phys.B810:503-526,2009
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, 6 figures, some changes to discussion and fixed typos in referencing (final NPB version)
Scientific paper
10.1016/j.nuclphysb.2008.09.038
The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition changing operator which governs Watts' computation is identified with a primary field which does not fit naturally within the extended Kac table. Instead a "shifted" extended Kac table is shown to be relevant. Augmenting the previously known logarithmic theory based on Cardy's crossing probability by this field, a larger theory is obtained, in which new classes of indecomposable rank-2 modules are present. No rank-3 Jordan cells are yet observed. A highly non-trivial check of the identification of Watts' field is that no Gurarie-Ludwig-type inconsistencies are observed in this augmentation. The article concludes with an extended discussion of various topics related to extending these results including projectivity, boundary sectors and inconsistency loopholes.
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