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Deformation Theory of Periodic Monopoles (With Singularities)

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Abstract

Cherkis and Kapustin (Commun Math Phys 218(2): 333–371, 2001 and Commun Math Phys 234(1):1–35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on \({\mathbb{R}^{2} \times \mathbb{S}^{1}}\) possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group \({SO(3)}\) are either empty or smooth hyperkähler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.

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  1. Mathematics Department, State University of New York at Stony Brook, Stony Brook, USA

    Lorenzo Foscolo

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  1. Lorenzo Foscolo
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Correspondence to Lorenzo Foscolo.

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Communicated by N. A. Nekrasov

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Foscolo, L. Deformation Theory of Periodic Monopoles (With Singularities). Commun. Math. Phys. 341, 351–390 (2016). https://doi.org/10.1007/s00220-015-2497-3

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