Abstract:
We study Bogomolny equations on ℝ2×?1. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperkähler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.
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Received: 20 July 2000 / Accepted: 29 November 2000
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Cherkis, S., Kapustin, A. Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory. Commun. Math. Phys. 218, 333–371 (2001). https://doi.org/10.1007/PL00005558
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DOI: https://doi.org/10.1007/PL00005558