Twistor Geometry and Field Theory

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U (2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.

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“…It has a geometrical interpretation in terms of holomorphic bundles over the twistor space P = R 4 × CP 1 for the space R 4 [37,38].…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, the gauge potential A is inert under a transformation ψ ± → ψ h ± ± := ψ ± h −1 ± , where h ± live in the complexified gauge group and are regular holomorphic on U ± , respectively. This is known as the twistor correspondence or the Euclidean version of Ward's theorem [37,38].…”

Section: Discussionmentioning

confidence: 99%

Noncommutative Instantons via Dressing and Splitting Approaches

Horváth

Lechtenfeld

Wolf

2002

J. High Energy Phys.

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“…In the purely bosonic case, one can introduce real (antihermitean) gauge fields on R 4 with a metric g of Euclidean signature (4, 0), Kleinian signature 46 Another possibility to obtain equation (8.15) is to use an action of holomorphic BF-type theories [42]. However, the relation of this kind of action with SFT is also unclear.…”

Section: Reality Conditions On the Quadricmentioning

confidence: 99%

“…Our considerations in this paper are based on the results of many authors (see e.g., and references therein). More details on twistor theory and the Penrose-Ward transform can be found in the books [44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

Popov¹,

Saemann²

2005

Advances in Theoretical and Mathematical Physics

108

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It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP 3|4 as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N = 4 super-Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N -extended SYM theory as the integrability of SYM fields on complex (2|N )-dimensional superplanes and demonstrate the equivalence of this description to Witten's formulation. The equivalence of the field equations of hCS theory on an open subset of CP 3|N to the field equations of self-dual N -extended SYM theory in four dimensions is made explicit. Furthermore, we extend the picture to the full N = 4 SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to the field equations of hCS theory on a quadric in CP 3|3 × CP 3|3 . e-print archive: http://lanl.arXiv.org/abs/arXiv:hep-th

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“…Unlike [19,21] and standard texts on Penrose's twistor theory [23], see e.g. [24], we avoid considering compactified complexified Minkowski space and its super-extensions, for these concepts are not relevant from the point of view of superconformal model-building we are interested in. Our 4D consideration is directly based on the use of (conformally) compactified Minkowski space S 1 × S 3 and its super-extensions.…”

Section: Introductionmentioning

confidence: 99%

On compactified harmonic/projective superspace, 5D superconformal theories, and all that

Kuzenko

2006

Nuclear Physics B

160

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Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building blocks which emerge in the transformation laws of primary superfields. Various off-shell superconformal multiplets are presented both in 5D harmonic and projective superspaces, including the so-called tropical (vector) multiplet and polar (hyper)multiplet. Families of superconformal actions are described both in the 5D harmonic and projective superspace settings. We also present examples of 5D superconformal theories with gauged central charge.

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Twistor Geometry and Field Theory

Cited by 346 publications

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Noncommutative Instantons via Dressing and Splitting Approaches

Noncommutative Instantons via Dressing and Splitting Approaches

On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

On compactified harmonic/projective superspace, 5D superconformal theories, and all that

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