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Nahm Transform for Periodic Monopoles and N=2 Super Yang-Mills Theory

Cherkis, Sergey and Kapustin, Anton (2001) Nahm Transform for Periodic Monopoles and N=2 Super Yang-Mills Theory. Communications in Mathematical Physics, 218 (2). pp. 333-371. ISSN 0010-3616. doi:10.1007/PL00005558.

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We study Bogomolny equations on R^2×S^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 N=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Cherkis, Sergey0000-0002-0785-0126
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2001 Springer-Verlag. Received: 20 July 2000; Accepted: 29 November 2000. We are grateful to Nigel Hitchin for a very helpful conversation concerning the definition of the monopole spectral data, and to Dmitri Orlov and Marcos Jardim for discussions. We also wish to thank the organizers of the workshop “The Geometry and Physics of Monopoles,” Edinburgh, August-September 1999, for creating a very stimulating atmosphere during the meeting and for providing us with an opportunity to present a preliminary version of this work. The work of S.Ch. was supported in part by NSF grant PHY9819686. The work of A.K. was supported in part by a DOE grant DE-FG02-90ER4054442.
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Department of Energy (DOE)DE-FG02-90ER4054442
Issue or Number:2
Record Number:CaltechAUTHORS:20160504-104759294
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66645
Deposited By: Tony Diaz
Deposited On:04 May 2016 20:25
Last Modified:11 Nov 2021 00:01

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