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Alex Bullivant (Maynooth University)

Title: Topological orders from centres in 3+1D

Abstract: In the work of Kong and Wen [1] it is conjectured that (n+1)D topological orders can be described algebraically by braided fusion n-categories, satisfying a condition called “remote detectability”. In this talk I will first describe the salient features of fusion n-categories as a categorification of semi-simple algebras. I will then describe a class of (3+1)D topological orders realised as the “center” of a fusion 2-category, categorifying the center of an algebra. Finally, I will relate such topological orders to those realised by a large class of exactly solvable Hamiltonian models, via the introduction of the tube 2-category.

[1] arXiv:1405.5858

Talk – Video

Talk – Slides