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

The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional Q Q -state Potts model. Four-point functions of the Potts conformal field theory are dictated by two constraints: the crossing-symmetry equation and S_Q S Q 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_Q S Q 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.