Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

We construct integrable lattice realizations of conformal twisted boundary conditions for ŝl(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.