Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of "interchiral conformal blocks", which arise from the degeneracy of fields with conformal weight h(r,1), with r is an element of N-*, and are related to the underlying presence of the "interchiral algebra" introduced in [2]. We also find evidence for the existence of "renormalized" recursions, replacing those that follow from the degeneracy of the field Phi 12D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.