Generalized string-nets for unitary fusion categories without tetrahedral symmetry

Understand

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system.

• However, the original construction is not applicable to all unitary fusion category since some additional symmetries for the $F$-symbols are imposed.
• In particular, the so-called tetrahedral symmetry is not fulfilled by many interesting unitary fusion categories.
• In this paper, we present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring these additional symmetries.