Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

Abstract

We construct integrable realizations of conformal twisted boundary conditions for ^sl(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) in (A_{g-2},A_{g-1},Γ) where Γis the group of automorphisms of G and g is the Coxeter number of G. Taking symmetries into account, these are identified with conformal twisted boundary conditions of Petkova and Zuber labelled by (a,b,γ) in (A_{g-2}xG, A_{g-2}xG,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 Potts (A_4,D_4) models.

11 pages, LaTeX. Added some references

References in corpus (4)

• Generalised twisted partition functions
• The many faces of Ocneanu cells
• Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
• Integrable Lattice Realizations of N=1 Superconformal Boundary Conditions

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