Refined Chern-Simons Theory and Knot Homology

Understand

The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds.

• It is defined via an index of the theory on N M5 branes, where the corresponding one-parameter deformation is a natural deformation of the geometric background.
• Analogously with the unrefined case, the solution of refined Chern-Simons theory is given in terms of S and T matrices, which are the proper Macdonald deformations of the usual ones.
• This provides a direct way to compute refined Chern-Simons invariants of a wide class of three-manifolds and knots.