Geometric construction of new Yang–Mills instantons over Taub-NUT space

Etesi, Gabor; Hausel, Tamás

doi:10.1016/s0370-2693(01)00821-8

Cited by 17 publications

(38 citation statements)

References 32 publications

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“…There was a number of attempts at construction of instantons on the Taub-NUT space. Some isolated solutions were found in [16,17] and particular families of solutions appear in [18,19,20]. We claim that the construction presented here produces all solutions for generic boundary conditions.…”

Section: Introductionmentioning

confidence: 62%

Moduli Spaces of Instantons on the Taub-NUT Space

Cherkis

2009

Commun. Math. Phys.

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We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.Comment: 26 pages, 7 figure

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Section: Introductionmentioning

confidence: 62%

Moduli Spaces of Instantons on the Taub-NUT Space

Cherkis

2009

Commun. Math. Phys.

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“…Recently new families of SU(2) Yang-Mills instantons on multi-Taub-NUT spaces have been found, cf. [29], [30]. In particular, [30] contains an intrinsic construction of the L 2 harmonic forms Ω i defined above as the curvatures of reducible SU (2) Yang-Mills instantons.…”

Section: Corollary 9 Suppose γ ⊂ Su(2) Is a Finite Cyclic Or Dihedramentioning

confidence: 99%

Hodge cohomology of gravitational instantons

Hausel¹,

Hunsicker²,

Mazzeo³

2004

Duke Math. J.

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134

271

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We study the space of L 2 harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on Qrank 1 ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The L 2 signature formula implied by our result is closely related to the one proved by Dai [25] and more generally by Vaillant [67], and identifies Dai's τ invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron [12] and the forthcoming paper of Cheeger and Dai [17]. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about L 2 harmonic forms in duality theories in string theory.

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“…This 2-form can be constructed as the exterior derivative of the metric dual of the Killing field generating an isometric action of U(1) on the 1-Taub-NUT space [10]. One can also obtain it by the conformal rescaling method when hunting for SU(2) anti-instantons [6]. Taking into account that H 2 (M V ; R) = {0} the condition dω = 0 is equivalent to the existence of an imaginary valued 1-form A such that dA = iω.…”

Section: Significance Of the Strong Holonomy Conditionmentioning

confidence: 99%

S-duality in Abelian gauge theory revisited

Etesi

Nagy

2011

Journal of Geometry and Physics

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Definition of the partition function of U(1) gauge theory is extended to a class of fourmanifolds containing all compact spaces and the asymptotically locally flat (ALF) ones including the multi-Taub-NUT sopaces. The partition function is calculated via zetafunction regularization and heat kernel techniques with special attention to its modular properties.In the compact case, compared with the purely topological result of Witten, we find a non-trivial curvature correction to the modular weights of the partition function. But S-duality can be restored by adding gravitational counter terms to the Lagrangian in the usual way.In the ALF case however we encounter non-trivial difficulties stemming from original non-compact ALF phenomena. Fortunately our careful definition of the partition function makes it possible to circumnavigate them and conclude that the partition function has the same modular properties as in the compact case.

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Geometric construction of new Yang–Mills instantons over Taub-NUT space

Cited by 17 publications

References 32 publications

Moduli Spaces of Instantons on the Taub-NUT Space

Moduli Spaces of Instantons on the Taub-NUT Space

Hodge cohomology of gravitational instantons

S-duality in Abelian gauge theory revisited

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