Topological Entanglement Entropy and Braids in Chern-Simons Theory

2017/07/20 by Hai Siong Tan, Tan, H. S.
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.1707.06629

openalex publication_date 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence

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