Deformations of Nearly Kähler Instantons

Charbonneau, Benoit; Harland, Derek

doi:10.1007/s00220-016-2675-y

Cited by 27 publications

(26 citation statements)

References 63 publications

(116 reference statements)

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“…Remark A.3. We note that the result of Lemma A.1 agrees with Proposition 7 of Charbonneau and Harland [9]. A similar argument in the case of S 7 shows that every (horizontal) deformation of the standard G 2 -instanton A 0 is of the form X ¬ F A 0 for a vector field on S…”

supporting

confidence: 81%

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$\mathrm{G}_2$-instantons on the 7-sphere

Waldron¹

2020

Preprint

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We study G 2 -instantons on the 7-sphere obtained by pullback from S 4 under the quaternionic Hopf fibration. The ASD instantons on S 4 with unit charge and structure group SU(2) generate a smooth, complete, 15-dimensional family of G 2 -instantons on S 7 . In general, we find that the space of infinitesimal deformations of a pullback to S 7 consists of three copies of the space of deformations on S 4 .

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confidence: 81%

“…Instantons on nearly parallel G 2 -manifolds have been studied by Harland and Nölle [15] and by Ball and Oliveira [6] in the case of Aloff-Wallach spaces. Ragini Singhal [18] also studies instantons on homogeneous nearly parallel G 2 -manifolds by similar methods to those of Charbonneau and Harland [9] for nearly Kähler 6-manifolds.…”

Section: )mentioning

confidence: 99%

$\mathrm{G}_2$-instantons on the 7-sphere

Waldron¹

2020

Preprint

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“…Then for τ ∈ Ω 1 (g E ) we have that (24) d A τ · η = 0, d * A τ = 0 if and only if D − T (τ · η) = 0 , as it happens in [5]. We define the following map…”

Section: Local Analysis Of the Moduli Space Of Spin(7)-instantonsmentioning

confidence: 99%

Transversality for the moduli space of Spin(7)-instantons

Muñoz

Shahbazi

2019

Rev. Math. Phys.

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We construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed 8-dimensional manifold endowed with a (possibly non-integrable) Spin (7)structure. We find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus. * F A = −F A ∧ Ω , Key words and phrases. Spin(7)-instanton, moduli space, Spin(7)-structure.

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“…Deformations of instanton bundles over G 2 manifolds have been studied before, see e.g. [34][35][36][37][38], and deformation studies of G structures with instantons also appeared recently in [39][40][41].…”

Section: Jhep11(2016)016 1 Introductionmentioning

confidence: 99%

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

Ossa

Larfors

Svanes

2016

J. High Energ. Phys.

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Abstract:We describe the infinitesimal moduli space of pairs (Y, V ) where Y is a manifold with G 2 holonomy, and V is a vector bundle on Y with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical G 2 cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli H 1 d A (Y, End(V )) plus the moduli of the G 2 structure preserving the instanton condition. The latter piece is contained in H 1 d θ (Y, T Y ), and is given by the kernel of a mapF which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the mapF is given in terms of the curvature of the bundle and maps, and moreover can be used to define a cohomology on an extension bundle of T Y by End(V ). We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on (Y, V ) when α = 0.

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Deformations of Nearly Kähler Instantons

Cited by 27 publications

References 63 publications

$\mathrm{G}_2$-instantons on the 7-sphere

$\mathrm{G}_2$-instantons on the 7-sphere

Transversality for the moduli space of Spin(7)-instantons

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

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