• conformal bootstrap
• conformal field theory
• potts model

We consider Conformal Field Theories with the global symmetry group of identical copies of Potts models. We derive the crossing equation for a scalar 4-point function. We use the numerical conformal bootstrap to derive rigorous and non-perturbative bounds on the scaling dimension of the lightest operators.
The interest in these CFTs is motivated by the critical properties of identical Potts models interacting with each other in two space-time dimensions. Since the CFT describing the critical fixed point is still not well characterised, we begin a comprehensive study using the top-down bootstrap approach.