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arXiv · 1807.09551

Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory

Alex Bullivant·João Faria Martins·Paul Martin
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Abstract

We show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduce a minimal categorification of biracks, which we call W-bikoids (welded bikoids). Our main example of W-bikoids arises from finite 2-groups, realised as crossed modules of groups. Given a W-bikoid, and hence a groupoid of symmetries, we construct a family of unitary representations of the loop braid group derived from representations of the groupoid algebra. We thus give a candidate for higher Bais' flux metamorphosis, and hence also a version of a `higher quantum group'.

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Alex Bullivant, João Faria Martins, Paul Martin. 2018-07-25. Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory. https://doi.org/10.4310/atmp.2019.v23.n7.a1

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