Saddle point equations in Seiberg-Witten theory

TL;DR

This paper proposes and solves saddle point equations for Seiberg-Witten curves in N=2 supersymmetric Yang-Mills theories across classical gauge groups, confirming their consistency with instanton calculations and known results.

Contribution

It introduces a unified approach to derive Seiberg-Witten curves for classical gauge groups and verifies their accuracy through explicit solutions and comparisons.

Findings

1-instanton corrections match direct computations

Equations successfully define Seiberg-Witten curves for various gauge groups

Most models' corrections agree with known results

Abstract

N=2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU(N), SO(N), and Sp(N) is considered. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for (almost) all models allowed by the asymptotic freedom the 1-instanton corrections which follows from these equations agree with the direct computations and with known results.