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Crystal Volumes and Monopole Dynamics

  • Sergey A. CherkisEmail author
  • Rebekah Cross
Article
  • 27 Downloads

Abstract

The low velocity dynamic of a doubly periodic monopole, also called a monopole wall or monowall for short, is described by geodesic motion on its moduli space. This moduli space is hyperkähler and non-compact. We establish a relation between the Kähler potential of this moduli space and the volume of a region in Euclidean three-space cut out by a plane arrangement associated with each monowall.

Notes

Acknowledgements

SCh is grateful to the organizers of the 2019 workshop “Microlocal Methods in Analysis and Geometry” at CIRM–Luminy and to the Institute des Hautes Études Scientifiques, Bures-sur-Yvette where the final stages of this work were completed. SCh received funding from the European Research Council under the European Union Horizon 2020 Framework Programme (h2020) through the ERC Starting Grant QUASIFT (QUantum Algebraic Structures In Field Theories) nr. 677368. RC thanks the Marshall Foundation for her Dissertation Fellowship funding.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of PhysicsUniversity of ArizonaTucsonUSA

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