Integrable and conformal boundary conditions for ℤk parafermions on a cylinder

Abstract

We study integrable and conformal boundary conditions for sℓ̂(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) ∈ (G, ℤ2k) are identified with associated integrable lattice boundary conditions labelled by (r, a) ∈ (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.