First-order equations for gauge fields in spaces of dimension greater than four

We consider LieG-valued Yang-Mills fields on the space R×G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold R×G/H carries a G 2 -structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in R 6 , R 4 or R 2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)×U(1), Sp(2)/Sp(1)×U (1) or G 2 /SU (3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S 1 ×G/H and dyons on iR×G/H are also given.

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“…Differentiating (2.1), we obtain the Yang-Mills equations with torsion, 2) where the torsion three-form H is defined by the formula * H := dΣ…”

Section: Yang-mills Equations With Torsionmentioning

confidence: 99%

Yang-Mills instantons and dyons on homogeneous G 2-manifolds

Bauer

Иванова²,

Lechtenfeld

et al. 2010

J. High Energ. Phys.

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“…Let M q be a real q-dimensional lorentzian manifold with nondegenerate metric of signature (− + · · · +), and S 2 ∼ = CP 1 the standard two-sphere of constant radius R. We shall consider the manifold M q × S 2 with local real coordinates x ′ = (x µ ′ ) ∈ R q on M q and coordinates ϑ ∈ [0, π], ϕ ∈ [0, 2π] on S 2 . In these coordinates the metric on M q × S 2 reads dŝ 2 = gμν dxμ dxν = g µ ′ ν ′ dx µ ′ dx ν ′ + R 2 dϑ 2 + sin 2 ϑ dϕ 2 , 1) where hatted indicesμ,ν, . .…”

Section: Yang-mills Equationsmentioning

confidence: 99%

“…In the presence of D-branes one encounters gauge theories in spacetime dimensionalities up to ten. Already more than 20 years ago, BPS-type equations in higher dimensions were proposed [1,2] as a generalization of the self-duality equations in four dimensions. For nonabelian gauge theory on a Kähler manifold the most natural BPS condition lies in the Donaldson-Uhlenbeck-Yau equations [3], which arise, for instance, in compactifications down to four-dimensional Minkowski spacetime as the condition for at least one unbroken supersymmetry.…”

Section: Introductionmentioning

confidence: 99%

Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions

Popov

Szabo

2006

Journal of Mathematical Physics

138

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We construct explicit BPS and non-BPS solutions of the Yang-Mills equations on the noncommutative space R 2n θ ×S 2 which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R 2n θ ×S 2 and nonabelian vortices on R 2n θ , which can be interpreted as a blowing-up of a chain of D0-branes on R 2n θ into a chain of spherical D2-branes on R 2n θ ×S 2 . The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.

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“…Here, the duality operator φ µνλρ is related to the structure constants of the octonions [1,2]. The self-dual Yang-Mills equations were considered in Euclidean gravity by replacing the Yang-Mills curvature with the curvature of the Riemannian 4-manifold.…”

mentioning

confidence: 99%

“…These equations imply Ricci flatness and thus their solutions obey Einstein's equations with zero cosmological constant. It is thus natural to consider the higher dimensional equations for self-duality [1,2] in the context of Euclidean gravity. That is the purpose of this note 3 .…”

mentioning

confidence: 99%

Self-duality inD<~8-dimensional Euclidean gravity

Acharya

O’Loughlin

1997

Phys. Rev. D

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In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU (2), SU (3), G 2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifolds is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory.

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First-order equations for gauge fields in spaces of dimension greater than four

Cited by 300 publications

References 7 publications

Yang-Mills instantons and dyons on homogeneous G 2-manifolds

Yang-Mills instantons and dyons on homogeneous G 2-manifolds

Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions

Self-duality inD<~8-dimensional Euclidean gravity

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