Calabi–Yau Monopoles for the Stenzel Metric

Oliveira, Gonçalo

doi:10.1007/s00220-015-2534-2

Cited by 18 publications

(41 citation statements)

References 9 publications

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“…In this section we provide a brief introduction to the Stenzel CY fourfold X 8 . For details, we refer to the articles [13,16]. The latter carries out the corresponding calculations in complex dimension 3.…”

Section: The Stenzel Manifoldmentioning

confidence: 99%

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Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric

Papoulias

2021

Commun. Math. Phys.

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We use the highly symmetric Stenzel Calabi–Yau structure on $$T^{\star }S^{4}$$ T ⋆ S 4 as a testing ground for the relationship between the Spin(7) instanton and Hermitian–Yang–Mills (HYM) equations. We reduce both problems to tractable ODEs and look for invariant solutions. In the abelian case, we establish local equivalence and prove a global nonexistence result. We analyze the nonabelian equations with structure group SO(3) and construct the moduli space of invariant Spin(7) instantons in this setting. This is comprised of two 1-parameter families—one of them explicit—of irreducible Spin(7) instantons. Each carries a unique HYM connection. We thus negatively resolve the question regarding the equivalence of the two gauge theoretic PDEs. The HYM connections play a role in the compactification of this moduli space, exhibiting a removable singularity phenomenon that we aim to further examine in future work.

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Section: The Stenzel Manifoldmentioning

confidence: 99%

“…For the classification of homogeneous bundles and invariant connections see ( [18], [13] Section 3.1, [10] Section 2.4). Our notation and conventions agree with the latter.…”

Section: So(5)-invariant Instantons With Structure Group U(1)mentioning

confidence: 99%

Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric

Papoulias

2021

Commun. Math. Phys.

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“…When it gets very large we expect them to resemble G 2 -instantons for the BS metric given in Theorem 7. When it gets very small, there may be a relation with Calabi-Yau monopoles on the deformed conifold (as in [21]). SU(2)/ SU(2) ∼ = S 3 in X = R 4 × S 3 .…”

Section: Solutions Smoothly Extending On P Idmentioning

confidence: 99%

“…One can see, under suitable assumptions, that G 2 -instantons on ALC G 2 -manifolds are asymptotic to Calabi-Yau monopoles on the Calabi-Yau cone. See [21] for some examples and results on Calabi-Yau monopoles in the asymptotically conical and conical settings.…”

Section: Remarkmentioning

confidence: 99%

SU(2)$$^2$$2-invariant $$G_2$$G2-instantons

Lotay¹,

Oliveira²

2018

Math. Ann.

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We initiate the systematic study of G 2 -instantons with SU(2) 2 -symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on R 4 × S 3 with its two explicitly known distinct holonomy G 2 metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We also give an explicit example of sequences of G 2 -instantons where "bubbling" and "removable singularity" phenomena occur in the limit.

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“…The analytic properties of the monopole equations in both these cases are work for the Ph.D. Thesis of the author. See [4] for examples of monopoles on a noncompact Calabi-Yau.…”

Section: Introductionmentioning

confidence: 99%

Monopoles on the Bryant–SalamonG2-manifolds

Oliveira

2014

Journal of Geometry and Physics

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a b s t r a c t G 2 -monopoles are solutions to gauge theoretical equations on noncompact 7-manifolds of G 2 holonomy. We shall study this equation on the 3 Bryant-Salamon manifolds. We construct examples of G 2 -monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the S 4 and CP 2 . These are the first nontrivial examples of G 2 -monopoles.Associated with each monopole there is a parameter m ∈ R + , known as the mass of the monopole. We prove that under a symmetry assumption, for each given m ∈ R + there is a unique monopole with mass m. We also find explicit irreducible G 2 -instantons on Λ 2 − (S 4 ) and on Λ 2 − (CP 2 ).The third Bryant-Salamon G 2 -metric lives on the spinor bundle over the 3-sphere. In this case we produce a vanishing theorem for monopoles.

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Calabi–Yau Monopoles for the Stenzel Metric

Cited by 18 publications

References 9 publications

Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric

Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric

SU(2)$$^2$$2-invariant $$G_2$$G2-instantons

Monopoles on the Bryant–SalamonG2-manifolds

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