Cardy states, defect lines and chiral operators of coset CFTs on the lattice

Abstract

We construct Cardy states, defect lines and chiral operators for rational coset conformal field theories on the lattice. The bulk theory is obtained by taking the overlap between tensor network representations of different string-nets, while the primary fields emerge from using the topological superselection sectors of the anyons in the original topological theory. This mapping provides an explicit manifestation of the equivalence between conformal field theories in two dimensions and topological field theories in three dimensions: their groundstates and elementary excitations are represented by exactly the same tensors.

Figures (4)

• Figure 1: Schematic overview of the relations between the concepts described in the main text, in the continuum (top) and on the lattice (bottom).
• Figure 2: Kac table of the tricritical Ising model; conventional notation (a), coset notation (b).
• Figure 3: Putting an MPO around the non-contractible loop of a cylinder with vacuum boundary conditions gives a single character partition function determined by the MPO, since pulling the MPO to the edge creates the boundary condition $\ket{a}$.
• Figure 4: Chiral operator insertion corresponding to the central idempotents on the lattice (a), eigenvector X of the transfer matrix with a defect projected onto one of the conformal towers (b). In the continuum, these two are related by a conformal transformation.