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Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations.
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S. K. Donaldson, “Nahm’s Equations and the Classification of Monopoles,” Commun. Math. Phys. 96
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P. B. Kronheimer, “Monopoles and Taub-NUT Metrics,” M. Sc. Thesis, Oxford, 1985
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N. J. Hitchin, A. Karlhede, U. Lindström and M. Roček, “Hyperkähler Metrics and Supersymmetry,” Commun. Math. Phys. 108
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M. F. Atiyah and N. J. Hitchin, “The Geometry and Dynamics of Magnetic Monopoles. M.B. Porter Lectures,” \href
1988
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P.B. Kronheimer, “A Hyperkähler Structure on the Cotangent Bundle of a Complex Lie Group,” MSRI preprint (1988)
1988
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P. B. Kronheimer, “The Construction of ALE Spaces as HyperKähler Quotients,” J. Diff. Geom. 29
1989
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P. J. Braam and P. van Baal, “Nahm’s Transformation for Instantons,” Commun. Math. Phys. 122
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J. Hurtubise, “The Classification of Monopoles for the Classical Groups,” Commun. Math. Phys. 120
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P. B. Kronheimer and H. Nakajima, “Yang-Mills Instantons on ALE Gravitational Instantons,” Math. Ann. 288
1990
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J. Hurtubise and M. K. Murray, “Monopoles and their Spectral Data,” Commun. Math. Phys. 133
1990
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S. K. Donaldson and P. B. Kronheimer, The Geomerty of Four-Manifolds
1990
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H. Nakajima, “Monopoles and Nahm’s equations,” \href
1990
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A. Maciocia, “Metrics on the Moduli Spaces of Instantons over Euclidean Four Space,” Commun. Math. Phys. 135
1991
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A. S. Dancer, “Dihedral Singularities and Gravitational Instantons,” J. Geom. Phys. 12
1993
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H. Nakajima, “Instantons on ALE spaces, Quiver Varieties, and Kac-Moody Algebras,” Duke Math. J. 76
1994
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A. S. Dancer, “A Family of Hyperkahler Manifolds,” Quarterly Journal of Mathematics 45
1994
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K. M. Lee and C. h. Lu, “SU(2) Calorons and Magnetic Monopoles,” Phys. Rev. D 58
1998
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R. Bielawski, “Asymptotic Metrics for SU(N)-monopoles with Maximal Symmetry Breaking,” Commun. Math. Phys. 199
1998
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R. Bielawski, “Monopoles and the Gibbons-Manton Metric,” Commun. Math. Phys. 194
1998
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S. A. Cherkis and A. Kapustin, “Singular Monopoles and Gravitational Instantons,” Commun. Math. Phys. 203
1999
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S. A. Cherkis and A. Kapustin, “D k
1999
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G. Etesi and T. Hausel, “Geometric Construction of New Taub-NUT Instantons,” Phys. Lett. B 514
2001
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E. Witten, “Sigma Models and the ADHM Construction of Instantons,” J. Geom. Phys. 15
1995
Cited alongside, same era.
H. Nakajima, “Instantons and Affine Lie Algebras,” Nucl. Phys. Proc. Suppl. 46
1996
Cited alongside, same era.
M. Bianchi, F. Fucito, G. Rossi and M. Martellini, “On the ADHM Construction on ALE Gravitational Backgrounds,” Phys. Lett. B 359
1996
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C. V. Johnson and R. C. Myers, “Aspects of Type IIB Theory on ALE Spaces,” Phys. Rev. D 55
1997
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D. E. Diaconescu, “D-branes, Monopoles and Nahm Equations,” Nucl. Phys. B 503
1997
Cited alongside, same era.
G. W. Gibbons and P. Rychenkova, “HyperKaehler Quotient Construction of BPS Monopole Moduli Spaces,” Commun. Math. Phys. 186
1997
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O. Biquard and M. Jardim, “Asymptotic Behaviour and the Moduli Space of Doubly-periodic Instantons,” Journal European Math. Soc. 3
2001
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N. Hitchin, “The Dirac Operator,” in Invitations to Geometry and Topology,
2002
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G. Etesi and T. Hausel, “New Yang-Mills Instantons over Multi-centered Gravitational Instantons,” Commun. Math. Phys. 235
2003
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2004
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S. A. Cherkis and N. J. Hitchin, “Gravitational Instantons of Type D k
2005
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2008
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H. Nakajima, “Quiver Varieties and Branching,” SIGMA 5
2009
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S. A. Cherkis, “Moduli Spaces of Instantons on the Taub-NUT Space,” Commun. Math. Phys. 290
2009
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E. Witten, “Branes, Instantons, and Taub-NUT Spaces,” JHEP 0906
2009
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