Integrable Lattice Realizations of Conformal Twisted Boundary Conditions

TL;DR

This work constructs integrable seam weights on A-D-E lattice models to realize conformal twisted boundary conditions for unitary minimal models on the torus. By fusing seams and incorporating graph automorphisms, the authors connect lattice realizations to Petkova-Zuber twisted partition functions within an Ocneanu quantum graph framework. They derive finite-size corrections that reproduce the conformal data and validate the approach with Ising and 3-state Potts examples, demonstrating numerical agreement of spectra and weights. The methodology provides a general path to realize twisted sectors for all A-D-E cases and sets the stage for a comprehensive treatment in CMOP2.

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.