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arXiv · 1404.5616

Parameter counting for singular monopoles on R^3

Gregory W. Moore·Andrew B. Royston·Dieter Van den Bleeken
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Abstract

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.

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Gregory W. Moore, Andrew B. Royston, Dieter Van den Bleeken. 2016-01-09. Parameter counting for singular monopoles on R^3. https://doi.org/10.1007/jhep10(2014)142

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