Topological Entanglement Entropy and Braids in Chern-Simons Theory
arXiv:1707.06629
Abstract
We explore a web of connections between quantum entanglement and knot theory by examining how topological entanglement entropy probes the braiding data of quasi-particles in Chern-Simons theory, mainly using gauge group as our working example. The problem of determining the Renyi entropy is mapped to computing the expectation value of an auxiliary Wilson loop in for each braid. We study various properties of this auxiliary Wilson loop for some 2-strand and 3-strand braids, and demonstrate how they reflect some geometrical properties of the underlying braids.
36 pages, 29 figure files; minor revisions