Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

Details Integrable Lattice Realizations of Conformal Twisted Boundary Conditions Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

2001-06-20

arxiv.org/abs/hep-th/0106182v4

Phys.Lett. B517 (2001) 429-435

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX. Added some references

Scientific paper

10.1016/S0370-2693(01)00982-0

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,\zeta) in (A_{g-2},A_{g-1},\Gamma) where \Gamma is 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,\gamma) 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.

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