Towards the Core of the Quantum Monopole

TL;DR

This paper investigates quantum monopole solutions in N=2 super Yang-Mills theories, deriving a differential equation for their core structure and exploring the nature of their quantum cores through numerical analysis.

Contribution

It introduces a first order differential equation for monopole moduli and examines the quantum core structure, addressing the limitations of the low-energy effective theory.

Findings

Derived a differential equation for monopole spatial dependence

Numerically analyzed monopole behavior near the quantum core

Explored the existence of modified monopole solutions without a strongly coupled core

Abstract

We study monopole solutions of the quantum exact low-energy effective N=2 super Yang-Mills theories of Seiberg and Witten. We find a first order differential equation for the spatial dependence of the moduli and show that it can be interpreted as an attractor equation. Numerically integrating this equation, we try to address the question of what happens when one approaches the quantum core of the monopole where the low energy effective theory breaks down or, alternatively, if there are modified monopole solutions that do not have a strongly coupled quantum core so that one may trust the solution not only asymptotically.