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arXiv · 1310.3028

Orbifold instantons, moment maps and Yang-Mills theory with sources

Tatiana A. Ivanova·Olaf Lechtenfeld·Alexander D. Popov·Richard J. Szabo
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Abstract

We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/\Gamma which are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kaehler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically-symmetric \Gamma-equivariant connections on complex V-bundles over R^4/\Gamma which are tailored to the way in which the orbifold group acts on the fibres. Some explicit abelian and nonabelian SU(2)-invariant solutions to the nstanton equations on the orbifold are worked out.

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Tatiana A. Ivanova, Olaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo. 2013-10-11. Orbifold instantons, moment maps and Yang-Mills theory with sources. https://doi.org/10.1103/physrevd.88.105026

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