Supersymmetric gauge theories in twistor space

Boels, Rutger H.; Mason, Lionel; Skinner, David

doi:10.1088/1126-6708/2007/02/014

Cited by 154 publications

(358 citation statements)

References 29 publications

(62 reference statements)

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“…Since these amplitudes are local one may wonder whether there is an action which has these amplitudes directly as vertices. In the field theory this can be derived from the usual Yang-Mills theory [22] by lifting to twistor space (see [23] for a review), and in the Abelian case this will be discussed briefly in section 4.…”

Section: Jhep11(2008)015mentioning

confidence: 99%

“…However, there may very well be some sense to be made of them. It should be noted though that in field theory it is not straightforward to derive the vanishing of the appropriate residues directly [41], despite the fact that this is known to be true from an independent action-based derivation of the N = 4 CSW rules [22,42] for all types of external particles.…”

Section: Field Theory Structures In String Theory Amplitudesmentioning

confidence: 99%

“…16 This was also recently advocated in [9] with a JHEP11(2008)015 different motivation. In field theory, the existence of MHV amplitudes and CSW rules for pure Yang-Mills theory in four dimensions is related to the existence of a gauge symmetry on twistor space which is not manifest from the space-time point of view [22]. In string theory, the Ward identity of ordinary gauge symmetry for on-shell amplitudes is a consequence of the world-sheet conformal symmetry.…”

Section: Field Theory Structures In String Theory Amplitudesmentioning

confidence: 99%

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MHV, CSW and BCFW: field theory structures in string theory amplitudes

Boels

Larsen

Obers³

et al. 2008

J. High Energy Phys.

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Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α ′ -corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α ′3 -correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

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Section: Jhep11(2008)015mentioning

confidence: 99%

Section: Field Theory Structures In String Theory Amplitudesmentioning

confidence: 99%

Section: Field Theory Structures In String Theory Amplitudesmentioning

confidence: 99%

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MHV, CSW and BCFW: field theory structures in string theory amplitudes

Boels

Larsen

Obers³

et al. 2008

J. High Energy Phys.

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“…Scattering amplitudes for N = 4 SYM can be obtained from a formulation of the theory via an action in twistor space that yields MHV diagrams as the Feynman diagrams [8,9]. In a separate development, it emerges that amplitudes can be obtained in a completely different way as certain correlation functions of Wilson loops in planar N = 4 SYM [3].…”

mentioning

confidence: 99%

Wilson Loop Diagrams and Positroids

Agarwala

Marin-Amat

2016

Commun. Math. Phys.

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Abstract:In this paper, we study a new application of the positive Grassmannian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N= 4 Super Yang-Mill theory (N = 4 SYM). There has been much interest in studying this theory via the positive Grassmannians using BCFW recursion. This is the first attempt to study MHV diagrams for planar Wilson loop calculations (or planar amplitudes) in terms of positive Grassmannians. We codify Wilson loop diagrams completely in terms of matroids. This allows us to apply the combinatorial tools in matroid theory used to identify positroids (non-negative Grassmannians) to Wilson loop diagrams. In doing so, we find that certain non-planar Wilson loop diagrams define positive Grassmannians. While non-planar diagrams do not have physical meaning, this finding suggests that they may have value as an algebraic tool, and deserve further investigation.

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“…There is for instance a natural 'space-time' gauge, which reduces the action to the space-time one. Fixing an axial gauge using a spinor η α for all the fields however leads directly to the CSW rules [15], including the full vertices.…”

Section: Twistor Actionsmentioning

confidence: 99%

CSW rules for massive matter legs and glue loops

Boels

Schwinn

2008

Nuclear Physics B - Proceedings Supplements

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Cachazo-Svrček-Witten-type Feynman rules for massive matter scalar legs and pure glue loops are presented, obtained by deriving them directly from the space-time action. We comment on the derivation and some sample applications, in particular to calculating one loop effects in pure Yang-Mills theory. Furthermore, we derive CSW rules for effective Higgs-gluon couplings studied in the literature. In addition, it is shown how twistor techniques for deriving canonical field transformations explored for massless scalars extend to massless fermions.

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Supersymmetric gauge theories in twistor space

Cited by 154 publications

References 29 publications

MHV, CSW and BCFW: field theory structures in string theory amplitudes

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Wilson Loop Diagrams and Positroids

CSW rules for massive matter legs and glue loops

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