High Energy Theory Seminar

We will study the entanglement structure of states in Chern-Simons (CS) theory obtained by performing the Euclidean path-integral on certain highly non-trivial 3-manifolds, namely link complements in S^3. This will allow us to assign an entanglement entropy to any bi-partition of an n-component link into sub-links; these entropies in fact provide framing independent link-invariants. In U(1) CS theory, we will give a general formula for the entanglement entropy across a bi-partition of a generic n-link into sub-links. In the non-Abelian SU(2) theory, we study various interesting 2 & 3-links including the Whitehead link and Borromean rings, both of which have non-trivial entanglement structures. If time permits, we will consider SL(2,C) and mention connections with gravity and hyperbolic geometry.