Abstract :
The logarithmic conformal field theory describing critical percolation is further explored using Wattsʹ determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition changing operator which governs Wattsʹ 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 Cardyʹs 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 Wattsʹ 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.
