A Note on the String Analog of $N=2$ Super-Symmetric Yang-Mills

TL;DR

This paper explores the relationship between string theory on a specific Calabi-Yau manifold and the quantum moduli space of N=2 SU(2) super Yang-Mills, highlighting the role of S-duality and geometric structures.

Contribution

It establishes a novel connection between the conifold locus in type II string theory and the quantum moduli space of N=2 super Yang-Mills, emphasizing the impact of S-duality transformations.

Findings

Identifies the conifold locus with the quantum moduli of N=2 SU(2) super Yang-Mills.

Shows the anomalous behavior of super Yang-Mills coordinates under S-duality.

Links string theory geometry with gauge theory dualities.

Abstract

A connection between the conifold locus of the type II string on the $W\:P_{11226}^4$ Calabi-Yau manifold and the geometry of the quantum moduli of $N = 2$ $SU(2)$ super Yang-Mills is presented. This relation is obtained from the anomalous behaviour of the $SU(2)$ super Yang-Mills special coordinates under $S$-duality transformation in $Sl(2;Z) / \Gamma_2$.