Parameter counting for singular monopoles on ℝ3

A bstract We compute the dimension of the moduli space of gauge-inequivalent solutions to the Bogomolny equation on ℝ 3 with prescribed singularities corresponding to the insertion of a finite number of ’t Hooft defects. We do this by generalizing the methods of C. Callias and E. Weinberg to the cas...

Full description

Saved in:
Bibliographic Details
Published inThe journal of high energy physics Vol. 2014; no. 10
Main Authors Moore, Gregory W., Royston, Andrew B., Van den Bleeken, Dieter
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 24.10.2014
Subjects
Classical and Quantum Gravitation
Elementary Particles
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
Wilson
t Hooft and Polyakov loops
Differential and Algebraic Geometry
Solitons Monopoles and Instantons
Online AccessGet full text

Cover

More Information
Summary:A bstract We compute the dimension of the moduli space of gauge-inequivalent solutions to the Bogomolny equation on ℝ 3 with prescribed singularities corresponding to the insertion of a finite number of ’t Hooft defects. We do this by generalizing the methods of C. Callias and E. Weinberg to the case of ℝ 3 with a finite set of points removed. For a special class of Cartan-valued backgrounds we go further and construct an explicit basis of ℒ 2 -normalizable zero-modes. Finally we exhibit and study a two-parameter family of spherically symmetric singular monopoles, using the dimension formula to provide a physical interpretation of these configurations. This paper is the first in a series of three on singular monopoles, where we also explore the role they play in the contexts of intersecting D-brane systems and four-dimensional N =2 super Yang-Mills theories.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2014)142