$SO/Sp$ Chern-Simons Gauge Theories At Large $N$, $SO/Sp$ Penner Models And The Gauge Group Volumes

TL;DR

This paper establishes a deep connection between large N $SO/Sp$ Chern-Simons theories and Penner models, deriving free energies and gauge group volume asymptotics from a unified framework.

Contribution

It introduces a deformed $SO/Sp$ Penner generating function linking $SO/Sp$ Chern-Simons theories and Penner models, providing new insights into their continuum limits and gauge group volumes.

Findings

Derived free energy and continuum limit from Penner model

Established equivalence of asymptotic gauge volume expansions

Connected gauge theories with Penner models through a deformed generating function

Abstract

We construct a deformed $SO/Sp$ Penner generating function responsible for the close connection between $SO/Sp$ Chern-Simons gauge theories at large $N$ and the $SO/Sp$ Penner models. This construction is then shown to follow from a sector of a Chern-Simons gauge theory with coupling constant $\lambda$. The free energy and its continuum limit of the perturbative Chern-Simons gauge theory are obtained from the Penner model. Finally, asymptotic expansions for the logarithm of the gauge group volumes are given for every genus $g\geq 0$ and shown to be equivalent to the continuum limits of the $SO/Sp$ Chern-Simons gauge theories and the $SO/Sp$ Penner models