Multi-boundary entanglement in Chern-Simons theory and link invariants

• DOI: 10.1007/jhep04(2017)061
• Publication Date: 2017-04-12T06:18:27Z
• Authors: Vijay Balasubrama...; Jackson R. Fliss; Robert G. Leigh; Onkar Parrikar
• Keywords: Linking number

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral defines a quantum state the boundary, in $n$-fold tensor product torus Hilbert space. focus case where is link-complement some $n$-component link inside three-sphere $S^3$. entanglement entropies resulting states define framing-independent invariants which are sensitive to topology chosen link. For Abelian ($G= U(1)_k$) we give general formula entropy associated an arbitrary $(m|n-m)$ partition generic into sub-links. involves number solutions certain Diophantine equations coefficients related Gauss linking numbers (mod $k$) between two sublinks. This connects simple concepts information theory, knot and shows that sublinks vanishes if only they have zero $k$). $G = SU(2)_k$, study various three component links. show 2-component Hopf maximally entangled, hence analogous Bell pair, Whitehead link, has linking, nevertheless entropy. Finally, Borromean rings "W-like" structure (i.e., tracing out one does not lead separable state), examples other 3-component links "GHZ-like" state).