Zesting produces modular isotopes and explains their topological invariants

Abstract

We show that the ribbon zesting construction can produce modular isotopes—different modular fusion categories with the same modular data. The result relies on the observation that the Reshetikhin–Turaev invariants of framed links associated to a ribbon fusion category satisfy a factorization property under zesting. This gives a new perspective on using topological invariants to classify topological order in light of modular data not being a complete invariant.