Braided zesting and its applications

Abstract

We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and minimal modular extensions of super-modular categories. Here we provide a complete obstruction theory and parameterization approach to the construction and illustrate its utility with several examples.

V1: 54 pages. V2 (Final version): Published in Communications in Mathematical Physics. This version includes a new Section 7 and several corrected misprints

References in corpus (3)

• Fermionic Modular Categories and the 16-fold Way
• On Gauging Symmetry of Modular Categories
• Rank-finiteness for modular categories

Cited by in corpus (9)

• Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six
• Reconstruction of modular data from $S{L}_2(\mathbb{Z})$ representations
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• 2-Drinfel'd double symmetry of the 4d Kitaev model
• $G$-crossed braided zesting
• Computing the group of minimal non-degenerate extensions of a super-Tannakian category
• The non-semisimple Kazhdan-Lusztig category for affine ${\mathfrak{sl}}_2$ at admissible levels
• Classification of integral modular data up to rank 13