Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories

TL;DR

This paper computes one-instanton corrections to the prepotential in N=2 super Yang-Mills theories using microscopic and exact methods, confirming results for classical gauge groups with low rank.

Contribution

It provides explicit one-instanton calculations for any simple Lie group and compares microscopic results with exact solutions for low-rank classical groups.

Findings

Microscopic and exact results agree for classical groups with rank ≤ 3.

Explicit one-instanton corrections are obtained for all simple Lie groups.

Analysis of Picard-Fuchs equations in the semi-classical regime.

Abstract

We study the low-energy effective theory in N=2 super Yang-Mills theories by microscopic and exact approaches. We calculate the one-instanton correction to the prepotential for any simple Lie group from the microscopic approach. We also study the Picard-Fuchs equations and their solutions in the semi- classical regime for classical gauge groups with rank r \leq 3. We find that for gauge groups G=A_r, B_r, C_r (r \leq 3) the microscopic results agree with those from the exact solutions.