Yang-Mills instantons on ALE gravitational instantons

Kronheimer, P. B.; Nakajima, Hiraku

doi:10.1007/bf01444534

Cited by 247 publications

(424 citation statements)

References 13 publications

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“…[82]) as the partition function of the supersymmetric quantum mechanics on the moduli space of Yang-Mills instantons on the ALE gravitational instantons R 4 /Γ γ , constructed in [64]. Here Γ γ ⊂ SU(2) is the MacKay dual to γ discrete group, whose representation theory is encoded in the quiver γ: Vert γ = Γ ∨ γ .…”

Section: Jhep03(2016)181mentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

213

466

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We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the qq-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of Ω-deformation and defects obey the Ward identities of two dimensional conformal field theory and its q-deformations. The details will be discussed in the companion papers.

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Section: Jhep03(2016)181mentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

213

466

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“…This is the plan of the paper: in section 2 we recall some details of the solution of N = 2, 2 * SYM theories on R 4 that will be important for the following. In this very section we also briefly recall the construction of gauge connections on ALE manifold which appeared in [20]. In section 3 we study the cohomologies of the moduli spaces of self dual gauge connections on ALE manifolds and compute the N = 4 partition function which turns out to be a modular form.…”

Section: Introductionmentioning

confidence: 99%

Multi-instanton calculus on ALE spaces

2004

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We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric N = 2, 2 * gauge theories on ALE spaces of the A n type. Furthermore we derive the Poincaré polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the N = 4 partition function which is a modular form in agreement with the expectations of SL(2, Z) duality.

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“…There are only very few SU(2) Yang-Mills instantons on Taub-NUT space found in the literature compared to the case of flat R 4 (see [18] and [1]) and in general to ALE spaces (see [21] and also [4]). There is a complete ADHM-Nahm data for the U(1)-invariant self-dual configuration on Taub-NUT space described in [7].…”

Section: Introductionmentioning

confidence: 99%

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

Etesi

Hausel

2001

Physics Letters B

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In this paper we exhibit a one-parameter family of new Taub-NUT instantons parameterized by a half-line. The endpoint of the half-line will be the reducible Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L 2 harmonic 2-form, while at an inner point we recover the Pope-Yuille instanton constructed as a projection of the LeviCivitá connection onto the positive su(2) + ⊂ so(4) subalgebra. Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for flat R 4 . That is we find a oneparameter family of harmonic functions on the Taub-NUT space with a point singularity, rescale the metric and project the obtained Levi-Civitá connection onto the other negative su(2) − ⊂ so(4) part. Our solutions will possess the full U (2) symmetry, and thus provide more solutions to the recently proposed U (2) symmetric ansatz of Kim and Yoon.

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Yang-Mills instantons on ALE gravitational instantons

Cited by 247 publications

References 13 publications

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Multi-instanton calculus on ALE spaces

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

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