Periodic Monopoles with Singularities and 𝒩=2 Super-QCD |
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Authors: | Sergey A. Cherkis Anton Kapustin |
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Affiliation: | (1) TEP, UCLA Physics Department, Los Angeles, CA 90095-1547, USA. E-mail: cherkis@physics.ucla.edu, US;(2) Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA. E-mail: kapustin@ias.edu, US |
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Abstract: | We study solutions of the Bogomolny equation on ℝ2×𝕊1 with prescribed singularities. We show that the Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperk?hler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain 𝒩=2 d=4 supersymmetric gauge theories on ℝ3×𝕊1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of the Bogomolny equation on ℝ2×𝕊1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane. Received: 9 March 2001 / Accepted: 15 January 2002 Published online: 20 January 2003 |
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