(Anti)self-dual gauge fields in dimensiond?4

Иванова, Т. А.; Popov, Alexander D.

doi:10.1007/bf01019334

Cited by 46 publications

(42 citation statements)

References 37 publications

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“…Some solutions for d>4 have been found, namely Spin(7)-instantons on R 8 in [48,49] and G 2 -instantons on R 7 in [50][51][52]. For generic non-integrable G-structures, the instanton equation implies the Yang-Mills equation with torsion.…”

Section: Jhep01(2015)030mentioning

confidence: 99%

“…The seven equations (4.17) restrict the space of admissible 2-forms, and the instanton bundle, which is locally isomorphic 3 to the subspace m, is spanned by This can be seen either by direct computation or by the explicit form of the projectors from so(6) to su(3) of [51]. Here we have used the Riemannian metric to pull up one of the indices of η 3 , and from here on we use e 6 = dr. A 6-dimensional representation of m can be chosen as in [22,64], Finally, the matrix equations for X µ read…”

Section: Jhep01(2015)030mentioning

confidence: 99%

“…Due to the properties of L we arrive at the following statement (cf. subsection 4.2): 51) implying that Γ su (2) and Γ P have the same components with respect to their adapted coframes e and e. Observe that the inhomogeneous part that is split off in the connection 1-form enters in the torsion (4.42) of Γ su (2) , thus altering the matrix equations. However, from (4.13) one can check that the local expressions of the respective field strengths of the extension of both Γ P and Γ su (2) by…”

Section: Transfer Of Solutionsmentioning

confidence: 99%

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Instantons on conical half-flat 6-manifolds

Bunk

Lechtenfeld

Popov

et al. 2015

J. High Energ. Phys.

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We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kähler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kähler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.

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Section: Jhep01(2015)030mentioning

confidence: 99%

Section: Jhep01(2015)030mentioning

confidence: 99%

Section: Transfer Of Solutionsmentioning

confidence: 99%

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Instantons on conical half-flat 6-manifolds

Bunk

Lechtenfeld

Popov

et al. 2015

J. High Energ. Phys.

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“…The concept of Yang-Mills instantons in four dimensions can be generalized by considering first-order equations for gauge potentials in spaces of dimension greater than four [19]- [24], [13,14], [25]- [29]. Most of these equations naturally appear in superstring theory and M-theory as the conditions for the survival of at least one unbroken supersymmetry in lowenergy effective field theory in d ≤ 4 dimensions.…”

Section: Su(4)-instanton Equations In Eight Dimensionsmentioning

confidence: 99%

Non-Abelian Vortices, Super Yang–Mills Theory and Spin(7)-Instantons

Popov¹

2010

Lett Math Phys

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We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R 2 × G/H, where G/H = SU(3)/U(1)×U(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R 2 × G/H and general solutions of non-Abelian coupled vortex equations on R 2 . These vortices are BPS solitons in a d = 4 gauge theory obtained from N = 1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R 2 , are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N = 4 super Yang-Mills theory and show that they have the same feature.

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“…An important role in this investigation is played by first-order gauge-field equations which are a generalization of the anti-self-duality equations in d = 4 to higher-dimensional manifolds with special holonomy (or, more generally, with G-structure [15,16]). Such equations were first introduced in [17] and further considered in [18][19][20][21][22] (see also the references therein).…”

Section: Introductionmentioning

confidence: 99%

Sigma-model limit of Yang–Mills instantons in higher dimensions

2015

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We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional Kähler manifold X which is a product Y ×Z of p-and q-dimensional Riemannian manifold Y and Z with p + q = 2n. We show that in the adiabatic limit, when the metric in the Z direction is scaled down, the gauge instanton equations on Y × Z become sigma-model instanton equations for maps from Y to the moduli space M (target space) of gauge instantons on Z if q ≥ 4. For q < 4 we get maps from Y to the moduli space M of flat connections on Z. Thus, the Yang-Mills instantons on Y × Z converge to sigma-model instantons on Y while Z shrinks to a point. Put differently, for small volume of Z, sigma-model instantons on Y with target space M approximate Yang-Mills instantons on Y × Z.

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(Anti)self-dual gauge fields in dimensiond?4

Cited by 46 publications

References 37 publications

Instantons on conical half-flat 6-manifolds

Instantons on conical half-flat 6-manifolds

Non-Abelian Vortices, Super Yang–Mills Theory and Spin(7)-Instantons

Sigma-model limit of Yang–Mills instantons in higher dimensions

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