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On the Energy Spectrum of Yang–Mills Instantons over Asymptotically Locally Flat Spaces

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Abstract

In this paper we prove that over an asymptotically locally flat (ALF) Riemannian four-manifold the energy of an “admissible” SU(2) Yang–Mills instanton is always integer. This result sharpens the previously known energy identity for such Yang–Mills instantons over ALF geometries. Furthermore we demonstrate that this statement continues to hold for the larger gauge group U(2).

Finally we make the observation that there might be a natural relationship between 4 dimensional Yang–Mills theory over an ALF space and 2 dimensional conformal field theory. This would provide a further support for the existence of a similar correspondence investigated by several authors recently.

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Authors and Affiliations

  1. Department of Geometry, Mathematical Institute, Faculty of Science, Budapest University of Technology and Economics, Egry J. u. 1, H ép., 1111, Budapest, Hungary

    Gábor Etesi

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  1. Gábor Etesi
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Correspondence to Gábor Etesi.

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Communicated by N. A. Nekrasov

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Etesi, G. On the Energy Spectrum of Yang–Mills Instantons over Asymptotically Locally Flat Spaces. Commun. Math. Phys. 322, 1–17 (2013). https://doi.org/10.1007/s00220-013-1754-6

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  • DOI: https://doi.org/10.1007/s00220-013-1754-6

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