Zesting produces modular isotopes and explains their topological invariants

TL;DR

This paper demonstrates that ribbon zesting can generate distinct modular fusion categories sharing the same modular data, providing insights into the classification of topological order beyond modular data alone.

Contribution

It introduces the concept of modular isotopes via ribbon zesting and explains their topological invariants, revealing limitations of modular data as a complete invariant.

Findings

Zesting can produce modular isotopes with identical modular data.

Reshetikhin-Turaev invariants factorize under zesting.

Modular data alone may not distinguish all topological phases.

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.