Global symmetry and conformal bootstrap in the two-dimensional $Q$-state Potts model

Abstract

The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional QQ-state Potts model. Four-point functions of the Potts conformal field theory are dictated by two constraints: the crossing-symmetry equation and S_QSQ symmetry. We numerically solve the crossing-symmetry equation for several four-point functions of the Potts conformal field theory for Q\in\mathbb{C}Q∈ℂ. In all examples, we find crossing-symmetry solutions that are consistent with S_QSQ symmetry of the Potts conformal field theory. In particular, we have determined their numbers of crossing-symmetry solutions, their exact spectra, and a few corresponding fusion rules. In contrast to our results for the O(n)O(n) model, in most of examples, there are extra crossing-symmetry solutions whose interpretations are still unknown.