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

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 ⩽ 3. We find that for gauge groups G = A r , B r , C r ( r ⩽ 3) the microscopic results agree with those from the exact solutions.