Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells

Understand

We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition.

• The lattice model is obtained by cutting the surface into triangles with clipped-off edges using open channel factorisation.
• The parameter is given by the hole radius.
• At finite radius, high energy states are suppressed and the model is effectively finite.