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 $Q$-state Potts model. Four-point functions of the Potts conformal field theory are dictated by two constraints: the crossing-symmetry equation and $S_Q$ symmetry. We numerically solve the crossing-symmetry equation for several four-point functions of the Potts conformal field theory for $Q\in \mathbb{C}$. In all examples, we find crossing-symmetry solutions that are consistent with $S_Q$ 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 $O(n)$ model, in most of examples, there are extra crossing-symmetry solutions whose interpretations are still unknown.

26 pages: v2, comments by referees and clarifications

References in corpus (2)

• Correlation functions in loop models
• Spaces of states of the two-dimensional O(n) and Potts models

Cited by in corpus (4)

• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• The tricritical Ising CFT and conformal bootstrap
• From combinatorial maps to correlation functions in loop models
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model