Penner Type Ensemble for Gauge Theories Revisited

TL;DR

This paper revisits the Penner type beta-ensemble for Omega-deformed N=2 SU(2) gauge theory, demonstrating how its partition function aligns with gauge theory results in strong coupling, confirming previous findings through saddle-point analysis.

Contribution

It provides a detailed saddle-point approximation of the Penner type beta-ensemble, connecting it to gauge theory partition functions and confirming prior results beyond tree-level.

Findings

Large N limit reproduces gauge theory partition function in strong coupling

Partition function matches results from special geometry and holomorphic anomaly

Leading terms of free energy at monopole/dyon point are derived

Abstract

The Penner type beta-ensemble for Omega-deformed N=2 SU(2) gauge theory with two massless flavors arising as a limiting case from the AGT conjecture is considered. The partition function can be calculated perturbatively in a saddle-point approximation. A large N limit reproduces the gauge theory partition function expanded in a strong coupling regime, for any beta and beyond tree-level, confirming previous results obtained via special geometry and the holomorphic anomaly equation. The leading terms and gap of the gauge theory free energy at the monopole/dyon point follow as a corollary.