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arXiv · 2107.08679

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

M. Y. Avetisyan·R. L. Mkrtchyan
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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 duality with refined topological strings.

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M. Y. Avetisyan, R. L. Mkrtchyan. 2021-07-19. On partition functions of refined Chern-Simons theories on $S^3$. https://arxiv.org/abs/2107.08679

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