Elsevier

Physics Letters B

Volume 517, Issues 3–4, 4 October 2001, Pages 429-435
Physics Letters B

Integrable lattice realizations of conformal twisted boundary conditions

https://doi.org/10.1016/S0370-2693(01)00982-0Get rights and content
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Abstract

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 ADE 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.

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