On certain aspects of string theory/gauge theory correspondence

TL;DR

This paper explores the Seiberg-Witten solutions for N=2 supersymmetric Yang-Mills theories across classical gauge groups, confirming instanton corrections and M-theory predictions at the 1-instanton level.

Contribution

It provides formal expressions for models with classical gauge groups and verifies the agreement of instanton corrections with direct and M-theory computations.

Findings

1-instanton corrections match direct calculations.

Seiberg-Witten curves derived and solved for several models.

M-theory predictions align with direct computations at 1-instanton level.

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 formal expression for almost all models accepted by the asymptotic freedom are obtained. The equations which define the Seiberg-Witten curve are proposed. In some cases they are solved. It is shown that for all considered the 1-instanton corrections which follows from these equations agree with the direct computations. Also they agree with the computations based on Seiberg-Witten curves which come from the M-theory consideration. It is shown that for a large class of models the M-theory predictions matches with the direct compuatations. It is done for all considered models at the 1-instanton level. For some models it is shown at the level of the Seiberg-Witten curves.