Deformations of Instanton Metrics
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss a class of bow varieties which can be viewed as Taub-NUT deformations of moduli spaces of instantons on {noncommutative} $\mathbb{R}^4$. Via the generalized Legendre transform, we find the Kähler potential on each of these spaces.
Keywords: instanton, bow variety, hyperkähler geometry, generalised Legendre transform.
@article{SIGMA_2023_19_a40,
     author = {Roger Bielawski and Yannic Borchard and Sergey A. Cherkis},
     title = {Deformations of {Instanton} {Metrics}},
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     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a40/}
}
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Roger Bielawski; Yannic Borchard; Sergey A. Cherkis. Deformations of Instanton Metrics. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a40/

[1] Adams M.R., Harnad J., Hurtubise J., “Isospectral Hamiltonian flows in finite and infinite dimensions. II. Integration of flows”, Comm. Math. Phys., 134 (1990), 555–585 | DOI | MR | Zbl

[2] Beauville A., “Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables”, Acta Math., 164 (1990), 211–235 | DOI | MR | Zbl

[3] Bielawski R., “Asymptotic metrics for ${\rm SU}(N)$-monopoles”, Comm. Math. Phys., 1999 (1998), 297–325, arXiv: hep-th/9801092 | DOI | MR

[4] Bielawski R., “Reducible spectral curves and the hyperkähler geometry of adjoint orbits”, J. Lond. Math. Soc., 76 (2007), 719–738, arXiv: math.DG/0605309 | DOI | MR | Zbl

[5] Bielawski R., “Line bundles on spectral curves and the generalised Legendre transform construction of hyperkähler metrics”, J. Geom. Phys., 59 (2009), 374–390, arXiv: 0806.0510 | DOI | MR | Zbl

[6] Cherkis S.A., “Instantons on the Taub-NUT space”, Adv. Theor. Math. Phys., 14 (2010), 609–641, arXiv: 0902.4724 | DOI | MR | Zbl

[7] Cherkis S.A., “Instantons on gravitons”, Comm. Math. Phys., 306 (2011), 449–483, arXiv: 1007.0044 | DOI | MR | Zbl

[8] Cherkis S.A., Larraín-Hubach A., Stern M., Instantons on multi-Taub-NUT spaces III: down transform, completeness, and isometry, in preparation | MR

[9] Donaldson S.K., “Nahm's equations and the classification of monopoles”, Comm. Math. Phys., 96 (1984), 387–407 | DOI | MR | Zbl

[10] Foscolo L., Ross C., Calorons and constituent monopoles, arXiv: 2207.08705

[11] Hitchin N.J., “On the construction of monopoles”, Comm. Math. Phys., 89 (1983), 145–190 | DOI | MR | Zbl

[12] Hitchin N.J., Karlhede A., Lindström U., Roček M., “Hyperkähler metrics and supersymmetry”, Comm. Math. Phys., 108 (1987), 535–589 | DOI | MR | Zbl

[13] Hurtubise J., “The classification of monopoles for the classical groups”, Comm. Math. Phys., 120 (1989), 613–641 | DOI | MR | Zbl

[14] Hurtubise J., Murray M.K., “On the construction of monopoles for the classical groups”, Comm. Math. Phys., 122 (1989), 35–89 | DOI | MR | Zbl

[15] Lee K., Weinberg E.J., Yi P., “Moduli space of many BPS monopoles for arbitrary gauge groups”, Phys. Rev. D, 54 (1996), 1633–1643, arXiv: hep-th/9602167 | DOI | MR | Zbl

[16] Lindström U., Roček M., “New hyper-Kähler metrics and new supermultiplets”, Comm. Math. Phys., 115 (1988), 21–29 | DOI | MR | Zbl

[17] Malyshev A.N., “Factorization of matrix polynomials”, Sib. Math. J., 23 (1982), 399–408 | DOI | MR

[18] Nakajima H., Lectures on Hilbert schemes of points on surfaces, Univ. Lecture Ser., 18, Amer. Math. Soc., Providence, RI, 1999 | DOI | MR | Zbl

[19] Nekrasov N., Schwarz A., “Instantons on noncommutative $\mathbb{R}^4$, and $(2,0)$ superconformal six-dimensional theory”, Comm. Math. Phys., 198 (1998), 689–703, arXiv: hep-th/9802068 | DOI | MR | Zbl

[20] Simpson C.T., “Moduli of representations of the fundamental group of a smooth projective variety. I”, Inst. Hautes Études Sci. Publ. Math., 79 (1994), 47–129 | DOI | MR | Zbl

[21] Takayama Y., “Bow varieties and ALF spaces”, Math. Proc. Cambridge Philos. Soc., 158 (2015), 37–82 | DOI | MR | Zbl