Duality relations for M coupled Potts models

We establish explicit duality transformations for systems of M q-state Potts models coupled through their local energy density, generalizing known results for M = 1,2,3. The M-dimensional space of coupling constants contains a self-dual submanifold of dimension D-M = [M/2]. For the case M = 4, the variation of the effective central charge along the self-dual surface is investigated by numerical transfer matrix techniques. Evidence is given for the existence of a family of critical points, corresponding to conformal field theories with an extended SM symmetry algebra.