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Spatially Periodic Instantons: Nahm Transform and Moduli

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Abstract

This paper establishes that the Nahm transform sending spatially periodic instantons (instantons on the product of the real line and a three-torus) to singular monopoles on the dual three-torus is indeed a bijection as suggested by the heuristic. In the process, we show how the Nahm transform intertwines to a Fourier–Mukai transform via Kobayashi–Hitchin correspondences. We also prove existence and non-existence results.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Physics and AstronomyUniversity of WaterlooWaterlooCanada
  3. 3.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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