Topological Phases Derived from Discrete Higher Gauge Theory and Representations of the Loop Braid Group

Joao Faria Martins

Lecturer in Algebra, School of Mathematics, University of Leeds

 

 

Abstract

Higher gauge theory is a higher order version of gauge theory which  enables the definition of non-abelian holonomy along surfaces embedded in a manifold.  After formulating the higher gauge theory version of the Kitaev quantum-double model, we show how  Aharonov-Bohm type effects of finite 2-group (3+1)-dimensional topological higher gauge theory  give rise to representations of the loop braid group.