Refined Chern-Simons versus Vogel universality. (English) Zbl 1283.58018

Krefl, Daniel; Schwarz, Albert

J. Geom. Phys. 74, 119-129 (2013).

Summary: We study the relation between the partition function of refined \(\mathrm{SU}(N)\) and \(\mathrm{SO}(2N)\) 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 \(\mathrm{SU}(N)\) and \(\mathrm{SO}(2N)\) Chern-Simons for special values of parameters. The large \(N\) expansion of the integral representation of refined \(\mathrm{SU}(N)\) 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.

MSC:

58J28

Eta-invariants, Chern-Simons invariants

Keywords:

refinement; Chern-Simons theory; topological strings

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