Genus one correction to Seiberg-Witten prepotential from \beta-deformed matrix model

TL;DR

This paper calculates genus one corrections to the free energy in eta-deformed matrix models with Penner potentials, demonstrating their agreement with Nekrasov partition functions for certain supersymmetric gauge theories.

Contribution

It provides explicit genus one corrections for eta-deformed matrix models and confirms their consistency with known gauge theory results.

Findings

Genus one free energy corrections match Nekrasov partition function results.

Explicit calculations for N_F=2,3,4 flavors.

Validates the eta-deformed matrix model approach to supersymmetric gauge theories.

Abstract

We study \beta-deformed matrix models with Penner type potentials, which correspond to N=2 SU(2) supersymmetric gauge theories with N_F=2,3, and 4 flavors. We compute explicitly the genus one corrections to the free energy of the matrix model and show that they match the corresponding results obtained from the Nekrasov partition function.