Integrable and Conformal Boundary Conditions for Zₖ Parafermions on a Cylinder

Original · EN

We study integrable and conformal boundary conditions for ˢl(2) Zₖ parafermions on a cylinder. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with negative spectral parameter. The conformal boundary conditions labelled by (a,m) in (G, Z₂ₖ) are identified with associated integrable lattice boundary conditions labelled by (r,a) in (Ag₋₂,G) where g is the Coxeter number of the A-D-E graph G. We obtain analytically the boundary free energies, present general expressions for the parafermion cylinder partition functions and confirm these results by numerical calculations.