Integrable and Conformal Boundary Conditions for Z_k Parafermions on a Cylinder

TL;DR

This paper investigates integrable and conformal boundary conditions for Z_k parafermions on a cylinder, linking lattice models with conformal field theories and providing analytical and numerical results for boundary free energies and partition functions.

Contribution

It establishes a correspondence between conformal and integrable boundary conditions for Z_k parafermions and derives analytical expressions for boundary free energies and partition functions.

Findings

Analytical boundary free energies derived.

Partition functions expressed in general form.

Numerical confirmation of theoretical results.

Abstract

We study integrable and conformal boundary conditions for ^sl(2) Z_k 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, Z_{2k}) are identified with associated integrable lattice boundary conditions labelled by (r,a) in (A_{g-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.