Integrable lattice realizations of conformal twisted boundary conditions

We construct integrable lattice realizations of conformal twisted boundary conditions for (sl) over cap (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,zeta) is an element of (A(g-2), A(g-1), Gamma) where Gamma 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, gamma) is an element of (A(g-2) circle times G, A(g-2) circle times G, Z(2)) and associated with nodes of the minimal analog of the Ocneanu quantum graph. Our results are illustrated using the Ising (A(2), A(3)) and 3-state Polls (A(4), D-4) models. (C) 2001 Elsevier Science B.V. All rights reserved.