Knot Homology from Refined Chern-Simons Theory

Understand

We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes.

• The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action.
• We give an explicit solution of the theory, in terms of a one-parameter refinement of the S and T matrices of Chern-Simons theory, related to the theory of Macdonald polynomials.
• The ordinary and refined Chern-Simons theory are similar in many ways; for example, the Verlinde formula holds in both.