On certain aspects of string theory/gauge theory correspondence

TL;DR

This thesis develops a comprehensive framework for non-perturbative effects in $\mathcal{N}=2$ super Yang–Mills with classical gauge groups $SU(N)$, $SO(N)$ and $Sp(N)$. It constructs a formal expression for the Wilsonian prepotential via localization, ADHM moduli, equivariant integration, and the $\Omega$-background, and derives the Seiberg–Witten curve data and 1-instanton corrections. The work demonstrates agreement between direct instanton calculations and results inferred from Seiberg–Witten curves and M-theory, establishing a broad, cross-checked computational platform for non-perturbative dynamics across multiple gauge groups and representations. It also connects the gauge theory prepotential to string/M-theory constructions through brane setups and universal bundle techniques, highlighting the deep interplay between field theory and geometry in the non-perturbative regime.

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.

Figures (6)

• Figure 1: The roadmap of the text
• Figure 2: $M$-theory setup for $SU(3)$ gauge theory
• Figure 3: Conformal map for $SU(3)$, $N_f=2$
• Figure 4: Basic cycles
• Figure 5: Conformal map for $Sp(1)$, $N_f=1$