Integrable lattice realizations of conformal twisted boundary conditions

We construct integrable lattice realizations of conformal twisted boundary conditions for sℓ̂(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical A–D–E lattice models with positive spectral parameter. The integrable seam boundary conditions are labelled by (r,s,ζ)∈(Ag−2,Ag−1,Γ) where Γ is the group of automorphisms of the graph G and g is the Coxeter number of G=A,D,E. Taking symmetries into account, these are identified with conformal twisted boundary conditions of Petkova and Zuber labelled by (a,b,γ)∈(Ag−2⊗G,Ag−2⊗G,Z2) and associated with nodes of the minimal analog of the Ocneanu quantum graph. Our results are illustrated using the Ising (A2,A3) and 3-state Potts (A4,D4) models.