Abstract
It is shown that calorons, or periodic instantons are the same as monopoles with the loop group as their structure group. Their twistor correspondences and spectral data are defined. The spectral data is shown to determine the general caloron.
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Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond. A362, 425–461 (1978)
Coppel, W.A.: Stability and asymptotic behaviour of differential equations. Boston, DC: Heath 1965
Chakrabarti, A.: Periodic generalizations of static self-dualSU(2) gauge fields. Phys. Rev. D35, 2, 696–706 (1987)
Garland, H., Hurtubise, J.C., Murray, M.K.: Calorons and rational maps. (to appear)
Hartshorne, R.: Algebraic geometry. Berlin, Heidelberg, New York: Springer 1977
Hitchin, N.J.: Monopoles and geodesics. Commun. Math. Phys.83, 579–602 (1982)
Hitchin, N.J.: On the construction of monopoles. Commun. Math. Phys.89, 145–190 (1983)
Hitchin, N.J., Murray, M.K.: Spectral curves and the ADHM construction. Commun. Math. Phys.114, 463–474 (1988)
Hurtubise, J.C.: Monopoles and rational maps. (to appear in Commun. Math. Phys. 1989)
Hurtubise, J.C., Murray, M.K.: On the construction of classical monopoles. (to appear in Commun. Math. Phys. 1988a)
Hurtubise, J.C., Murray, M.K.: Monopoles and their spectral data (to appear 1988b)
Macdonald, I.G.: Affine Lie algebras and modular forms. Seminaire Bourbaki 33e annee 1980/81 no 577
Murray, M.K.: Non-abelian magnetic monopoles. Commun. Math. Phys.96, 539–565 (1984)
Nahm, W.: Self-dual monopoles and calorons. Preprint Bonn-University Bonn-HE-83-16. September 1983
Segal, G., Pressley, A.N.: Loop groups. Oxford: Oxford University Press 1987
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Communicated by A. Jaffe
Research supported in part by NSF grant DMS-8506130
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Garland, H., Murray, M.K. Kac-Moody monopoles and periodic instantons. Commun.Math. Phys. 120, 335–351 (1988). https://doi.org/10.1007/BF01217968
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DOI: https://doi.org/10.1007/BF01217968