# Magnetic charge quantization from SYM considerations

## TL;DR

This paper demonstrates that magnetic charge quantization in supersymmetric Yang-Mills theories can be derived from symmetry and gauge invariance principles, linking topological magnetic charges with field theory considerations.

## Contribution

It establishes a novel connection between magnetic charge quantization and supersymmetry gauge invariance, particularly through the role of Fayet-Iliopoulos parameters.

## Key findings

- Magnetic charges satisfy Dirac quantization in D3-D3' systems.
- Quantization condition can be derived from SUSY and gauge invariance arguments.
- FI parameter is proportional to magnetic charge and is quantized.

## Abstract

An intersecting D3-D3' system contains magnetic monopole solutions due to D- strings stretched between two branes. These magnetic charges satisfy the usual Dirac quantization relation. We show that this quantization condition can also be obtained directly by SUSY and gauge invariance arguments of the theory and conclude that the independence of physics from a shift of holonomy is exactly equivalent to regarding a {\it Fayet-Iliopoulos (FI) gauge} for our set-up. So we are led to conjecture that there is a correspondence between the topological point of view of magnetic charges and SYM considerations of their theories. This picture implies that one can attribute a definite quantity to the integration of the vector multiplet over the singular region such that we can identify it with magnetic flux. It also indicates that the FI parameter is proportional to the magnetic charge so it is a quantized number.