Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

TL;DR

This paper constructs integrable lattice models that realize conformal twisted boundary conditions in minimal models, linking lattice boundary conditions with conformal field theory and illustrating with Ising and 3-state Potts models.

Contribution

It introduces a method to realize conformal twisted boundary conditions through integrable lattice models, connecting algebraic labels with physical boundary conditions.

Findings

Constructed integrable lattice realizations for conformal twisted boundary conditions.

Linked lattice boundary labels with conformal field theory labels.

Demonstrated the approach on Ising and 3-state Potts models.

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,\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.