The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation

TL;DR

This paper develops a perturbative matrix model approach to compute low-energy quantities in N=2 U(N) gauge theory, including periods and prepotential, without relying on the Seiberg-Witten curve, and verifies results up to first instanton order.

Contribution

It introduces a perturbative matrix model method to calculate gauge theory periods and prepotential, bypassing the need for Seiberg-Witten geometric data.

Findings

Successfully defines periods via tadpole diagrams perturbatively.

Computes the prepotential up to first instanton level with agreement to known results.

Provides a new perturbative framework for low-energy gauge theory analysis.

Abstract

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N=2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a_i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-Witten differential or curve. We also compute the N=2 prepotential F(a) perturbatively up to the first-instanton level finding agreement with the known result.