Non-self-dual gauge fields

Isenberg, James; Yasskin, Philip B.; Green, Paul S.

doi:10.1016/0370-2693(78)90486-0

Cited by 110 publications

(93 citation statements)

References 5 publications

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“…Mason and Skinner gave an ambitwistor formulation for pure Yang-Mills, whose ambitwistor Lagrangian contains a triple derivative of a delta function δ ′′′ (Z · W ). The fact that the equations of motion of pure Yang-Mills theory correspond to extensions to the triple neighborhood about the Z · W = 0 locus has been known before from work by Witten [51] and Isenberg, Iasskin and Green [52]. The derivatives of the delta functions serve to cancel the twistor scaling which in the supersymmetric case was canceled by integrations over odd variables.…”

Section: Discussionmentioning

confidence: 98%

Twistors, harmonics and holomorphic Chern-Simons

Schwab

Vergu

2013

J. High Energ. Phys.

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We show that the off-shell N = 3 action of N = 4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator∂ is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time operators can be written as a Penrose transform on the coset SU(3)/(U(1) × U(1)). We observe a strong similarity to ambitwistor space constructions.

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Section: Discussionmentioning

confidence: 98%

Twistors, harmonics and holomorphic Chern-Simons

Schwab

Vergu

2013

J. High Energ. Phys.

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“…Such an interpretation was proposed in the papers by Manin [5], Witten [6] and Isenberg-Green-Yasskin [7]. To present their construction, denote by (P 3 ) * the dual projective space identified with the space of complex projective planes P 2 in P 3 .…”

Section: Twistor Description Of Yang-mills Fieldsmentioning

confidence: 99%

“…The twistor description of Yang-Mills fields was proposed in the papers by Manin [5], Witten [6] and Isenberg-Green-Yasskin [7]. They are interpreted as holomorphic vector bundles over the incidence quadric in P 3 × (P 3 ) * with some special properties described below.…”

Section: Introductionmentioning

confidence: 99%

Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

Сергеев

2015

Mathematics

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Abstract:We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang-Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the loop space ΩG of a compact Lie group G and the moduli space of Yang-Mills G-fields on R 4 .

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“…In [4,5] Isenberg et al and Manin have studied gauge fields whose curvature is neither self-dual nor anti-self-dual. We miss however actual examples of the theory and this we will give in this note.…”

Section: Construction Of a Family Of Non-self-dual Gauge Fields Ignacmentioning

confidence: 99%

Construction of a family of non-self-dual gauge fields

Sols¹

1986

Trans. Amer. Math. Soc.

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Abstract. Using the generalization of vector bundles by reflexive sheaves recently introduced by R. Hartshorne in [2] we construct a 15-dimensional family of nontrivial complex gauge fields (U, £,V) which are not self-dual nor anti-self-dual.(1/ is an affine neighborhood in Qt = Gr(2, C4) of the stereographic compactification S4 of R4, E is a vector bundle on U and v is a connection on it whose curvature satisfies the inequalities * * and * * -.)In [4,5] Isenberg et al. and Manin have studied gauge fields whose curvature is neither self-dual nor anti-self-dual. We miss however actual examples of the theory and this we will give in this note. Moreover, we introduce in twistor theory the tool of reflexive sheaves (a kind of vector bundle with singularities) whose interest is very recent in geometry, and they seem to play a roll also in this context. We start by recalling the characterizations of such fields, which are well known by now. We use the language of coherent sheaves [1].The complexification of the stereographic compactification S4 of R4 is the complex 4-dimensional projective smooth quadric Q4. This is usually referred to by geometers as the Klein quadric. It can also be viewed as the Grassmann variety parametrizing all lines in projective space P3 = P(C4) and S4 as the subset of points corresponding to the lines L = PX(V) such that V = C2 is invariant under the antiholomorphic map C4 -» C4 consisting of multiplication by j g H (quaternions) when we decompose C4sH ffi^'H.Our construction depends on 14 complex parameters and produces an affine neighborhood U of S4 in <24 and a vector bundle on U together with with a connection on it whose curvature is neither self-dual (*<¡> ¥= ) nor anti-self-dual

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Non-self-dual gauge fields

Cited by 110 publications

References 5 publications

Twistors, harmonics and holomorphic Chern-Simons

Twistors, harmonics and holomorphic Chern-Simons

Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

Construction of a family of non-self-dual gauge fields

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