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

• Main Authors: M.Y. Avetisyan, R.L. Mkrtchyan
• Format: Article
• Language: English
• Published: SpringerOpen 2021-10-01
• Series: Journal of High Energy Physics
• Subjects: Chern-Simons Theories; Topological Field Theories; Topological Strings
• Online Access: https://doi.org/10.1007/JHEP10(2021)033

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S 3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the 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 the refined topological strings.