Topological Entanglement Entropy and Braids in Chern-Simons Theory
arXiv: High Energy Physics - Theory(2017)
摘要
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 SU(2) 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 S^3 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.
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