Abstract
We compute the dimension of the moduli space of gauge-inequivalent solutions to the Bogomolny equation on ℝ3 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 ℝ3 with a finite set of points removed. For a special class of Cartan-valued backgrounds we go further and construct an explicit basis of ℒ2-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 \( \mathcal{N} \) =2 super Yang-Mills theories.
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Moore, G.W., Royston, A.B. & Van den Bleeken, D. Parameter counting for singular monopoles on ℝ3 . J. High Energ. Phys. 2014, 142 (2014). https://doi.org/10.1007/JHEP10(2014)142
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DOI: https://doi.org/10.1007/JHEP10(2014)142