On two approaches to 3-dimensional TQFTs

TL;DR

This paper proves an equivalence between two different 3-dimensional topological quantum field theory (TQFT) invariants derived from a spherical fusion category and its Drinfeld center, unifying two approaches in TQFT.

Contribution

It establishes that the Turaev-Viro-Barrett-Westbury state sum invariant equals the Reshetikhin-Turaev invariant for the Drinfeld center, linking these two constructions.

Findings

Proved the equality of TQFT invariants from C and Z(C).

Unified two approaches to 3D TQFTs.

Strengthened the theoretical understanding of TQFT invariants.

Abstract

Let C be a spherical fusion category. We prove that the Turaev-Viro-Barrett-Westbury state sum invariant of 3-manifolds derived from C is equal to the Reshetikhin-Turaev surgery invariant of 3-manifolds derived from Z(C), where Z(C) is the Drinfeld-Joyal-Street center of C.