Refined Chern–Simons versus Vogel universality

We study the relation between the partition function of refined SU(N)SU(N) and SO(2N)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)SU(N) and SO(2N)SO(2N) Chern–Simons for special values of parameters. The large NN expansion of the integral representation of refined SU(N)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=1c=1 string free energy.