Self-Dual Super-Yang-Mills as a String Theory in (<i>x</i>, ) Space

Berkovits, Nathan

doi:10.1088/1126-6708/2004/05/034

Cited by 11 publications

(13 citation statements)

References 34 publications

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“…Following various proposals, e.g. [4,35,57,58] (see also references therein), one can extend it to be spacetime supersymmetric. This is believed to lead to an explicit relation between the supersymmetric extension of N = 4 topological string theory and the N = 2 topological string (B-type) [5], but the picture is far from being complete.…”

Section: Discussionmentioning

confidence: 99%

“…will look like 4) and, multiplying the expansion in λ + by λ ṅ 1 (or the expansion in λ − by λ ṅ 2 ), one obtains a homogeneous polynomial of degree n:…”

Section: Discussionmentioning

confidence: 99%

“…Here, Y is a subspace of CP 3|4 parametrized by three complex bosonic coordinates together with their complex conjugate and four (holomorphic) fermionic coordinates, Ω is a holomorphic measure for bosonic and fermionic coordinates, andÂ 0,1 is the (0, 1)-component of a connection one-formÂ on a rank n complex vector bundle E over CP 3|4 depending on both the bosonic and fermionic coordinates. It was shown [2] that there is a bijection between the moduli spaces of hCS theory (1.2) on the supermanifold CP 3|4 \CP 1|4 and of self-dual N = 4 super-Yang-Mills (SYM) theory on the space R 4 with a metric of signature (+ + + +) or (− − + +), depending on the reality conditions imposed on the supertwistor space (for related works see [3][4][5][6][7][8][9][10]). It was also demonstrated that the above twistor description allows one to recover Yang-Mills scattering amplitudes, in particular, maximally helicity violating (MHV) ones, 2 and to clarify the holomorphicity…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…will look like 4) and, multiplying the expansion in λ + by λ ṅ 1 (or the expansion in λ − by λ ṅ 2 ), one obtains a homogeneous polynomial of degree n:…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Therefore, z ± singular strings may carry the Chan-Paton factors (chiral currents and traveling waves) which will play the role of quarks with respect to the complex string. It should be noted that the (x, θ) string was discussed in the papers [7,9,2,28] as a prospective alternative for the twistor-string. …”

Section: Complex Kerr Stringmentioning

confidence: 99%

“…In sec.4 the twistorial structure of the Kerr geometry is discussed. In Sec.5 we consider the complex Kerr geometry and show that it contains a version of the complex twistor-string which has some properties of the well known N=2 string [6] and also the chiral (x, θ) twistor-string [7,8,9,10]. Being imbedded into M 4 , this string turns out to be open with a partially broken N=2 supersymmetry.…”

Section: Introductionmentioning

confidence: 99%

Rotating black hole, twistor-string and spinning particle

Burinskii

2005

Czech J Phys

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We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial real stringy structure consisting of the Kerr circular string and an axial stringy system.We consider also the complex and twistorial structures of the Kerr geometry and show that there is a complex twistor-string built of the complex N=2 chiral string with a twistorial (x, θ) structure. By imbedding into the real Minkowski M 4 , the N=2 supersymmetry is partially broken and string acquires the open ends. Orientifolding this string, we identify the chiral and antichiral structures. Target space of this string is equivalent to the Witten's 'diagonal' of the CP 3 × CP * 3 .

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