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Topological Entanglement Entropy and Braids in Chern-Simons Theory (1707.06629v2)
Published 20 Jul 2017 in hep-th, math-ph, math.MP, and quant-ph
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 $SU(2)$ 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 $S3$ 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.