On partition functions of refined Chern-Simons theories on $S^3$

Abstract

We present a new expression for the partition function of refined Chern-Simons theory on S 3 with arbitrary gauge group, which is explicitly equal to 1, when the coupling constant is zero. Using this form of partition function we show that the previously known Krefl-Schwarz representation of partition function of refined Chern-Simons theory on S 3 can be generalized to all simply-laced algebras.For all non-simply-laced gauge algebras we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of a duality with refined topological strings.