Refined Chern-Simons versus Vogel universality

TL;DR

This paper explores the connection between refined Chern-Simons theories for SU(N) and SO(2N) groups and the universal Chern-Simons framework, introducing a four-parameter generalization that links to string theory concepts.

Contribution

It introduces a four-parameter integral representation unifying refined SU(N) and SO(2N) Chern-Simons theories within the universal Chern-Simons framework.

Findings

Derived a four-parameter generalization of universal Chern-Simons integral representation.

Explicitly showed the large N expansion relates to refined Euler characteristics.

Connected refined Chern-Simons partition functions to deformed string free energy.

Abstract

We study the relation between the partition function of refined SU(N) and SO(2N) Chern-Simons on the 3-sphere and the universal Chern-Simons partition function in the sense of Mkrtchyan and Veselov. We find a four-parameter generalization of the integral representation of universal Chern-Simons that includes refined SU(N) and SO(2N) Chern-Simons for special values of parameters. The large N expansion of the integral representation of refined SU(N) Chern-Simons explicitly shows the replacement of the virtual Euler characteristic of the moduli space of complex curves with a refined Euler characteristic related to the radius deformed c=1 string free energy.