Brane bending and monopole moduli

TL;DR

This paper explores how intersecting brane systems model singular monopoles in four-dimensional Yang-Mills-Higgs theory, providing insights into their moduli spaces, dimension formulas, and dynamic phenomena like monopole bubbling.

Contribution

It offers a brane-based physical interpretation of monopole moduli spaces, including conditions for non-empty moduli spaces and the effects of 't Hooft defects, along with new dynamical phenomena.

Findings

Brane constructions validate conditions for non-empty monopole moduli spaces.

Physical intuition for dimension formulas and defect contributions.

Discovery of monopole extraction and bubbling phenomena.

Abstract

We study intersecting brane systems that realize a class of singular monopole configurations in four-dimensional Yang-Mills-Higgs theory. Singular monopoles are solutions to the Bogomolny equation on R^3 with a prescribed number of singularities corresponding to the insertion of 't Hooft defects. We use the brane construction to motivate a recent conjecture on the conditions for which the moduli space of solutions is non-empty. We also show how branes provide physical intuition for various aspects of the dimension formula derived in {arXiv:1404.5616}, including the contribution to the dimension from the defects and its invariance under Weyl reflections of the 't Hooft charges. Along the way we uncover and illustrate new dynamical phenomena for the brane systems, including a description of smooth monopole extraction and bubbling from 't Hooft defects.