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Journal Article

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


Brehm,  Enrico M.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Brehm, E. M., & Runkel, I. (2022). Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells. Journal of physics A, 55(23): 235001. doi:10.1088/1751-8121/ac6a91.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B498-0
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. In the zero-radius limit, it recovers the CFT
amplitude exactly. In the touching hole limit, one obtains a topological field
If one chooses a special conformal boundary condition which we call "cloaking
boundary condition", then for each value of the radius the fusion category of
topological line defects of the CFT is contained in the lattice model. The fact
that the full topological symmetry of the initial CFT is realised exactly is a
key feature of our lattice models.
We provide an explicit recursive procedure to evaluate the interaction vertex
on arbitrary states. As an example, we study the lattice model obtained from
the Ising CFT on a torus with one hole, decomposed into two lattice cells. We
numerically compare the truncated lattice model to the CFT expression obtained
from expanding the boundary state in terms of the hole radius and we find good
agreement at intermediate values of the radius.