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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.
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We discuss the worldvolume description of intersecting D-branes, including the metric on the moduli space of deformations. We impose a choice of static gauge that treats all the branes on an equal footing and describes the intersection of D-branes as an embedded special Lagrangian three-surface. Some explicit solutions to these equations are given and their interpretation in terms of a superpotential on moduli space is discussed. These surfaces arise from flat direction of a non-Abelian superpotential and imply the existance of non-compact G_2 manifolds.
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We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.
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