Speaker
Description
Wilson loops in the 3d SU(2) Chern–Simons theory with the integration contour being an arbitrary link can be computed as a sum over closed circles formed by the planar resolution of vertices in a knot diagram. This method can be straightforwardly lifted from SU(2) to SU(N) at an arbitrary N – but for a special class of bipartite diagrams made entirely from the anitparallel lock tangle. Many amusing and important knots and links can be described in this way, from twist and double braid knots to the celebrated Kanenobu knots for even parameters – and for all of them the entire Wilson loops possess planar decomposition. This provides an approach to evaluation of Wilson loops. Moreover, this planar calculus is also applicable to other symmetric representations beyond the fundamental one, and to links which are not fully bipartite.
