scholarly journals A twistor space action for Yang-Mills theory

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Alexander D. Popov
Keyword(s):  
Twistor Space ◽  
Yang Mills ◽  
Space Action

scholarly journals Fourier transform from momentum space to twistor space

2020 ◽  
pp. 2150032
Author(s):  
Jun-ichi Note
Keyword(s):  
Fourier Transform ◽  
Momentum Space ◽  
Twistor Space ◽  
Three Dimensional ◽  
Yang Mills ◽  
The Fourier Transform ◽  
Complex Integral ◽  
Cech Cohomology ◽  
Complex Projective ◽  
Operator Representations

Several methods use the Fourier transform from momentum space to twistor space to analyze scattering amplitudes in Yang–Mills theory. However, the transform has not been defined as a concrete complex integral when the twistor space is a three-dimensional complex projective space. To the best of our knowledge, this is the first study to define it as well as its inverse in terms of a concrete complex integral. In addition, our study is the first to show that the Fourier transform is an isomorphism from the zeroth Čech cohomology group to the first one. Moreover, the well-known twistor operator representations in twistor theory literature are shown to be valid for the Fourier transform and its inverse transform. Finally, we identify functions over which the application of the operators is closed.

TWISTORS, YANG-MILLS AMPLITUDES AND LANDAU LEVELS

2005 ◽  
Vol 20 (27) ◽  
pp. 6107-6121
Author(s):  
V. P. NAIR
Keyword(s):  
Twistor Space ◽  
Point Of View ◽  
Wave Functions ◽  
Landau Levels ◽  
Holomorphic Curves ◽  
Short Discussion ◽  
Yang Mills ◽  
Lowest Landau Level ◽  
Recent Developments ◽  
Discussion Review

We give a short discussion/review of the recent developments expressing the perturbative scattering amplitudes in Yang-Mills theory, specifically for the [Formula: see text] theory, in terms of holomorphic curves in a supersymmetric twistor space. Holomorphic curves, which are maps of CP1 to the supertwistor space, can also be interpreted as the lowest Landau level wave functions; this point of view is also briefly explained.

YANG-MILLS AMPLITUDES FROM STRING THEORY IN TWISTOR SPACE

2005 ◽  
Vol 20 (15) ◽  
pp. 3416-3419 ◽  
Author(s):  
MARCUS SPRADLIN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Twistor Space ◽  
Mathematical Structure ◽  
Feynman Diagrams ◽  
Tree Level ◽  
Algebraic Equations ◽  
Yang Mills

Tree-level gluon scattering amplitudes in Yang-Mills theory frequently display simple mathematical structure which is completely obscure in the calculation of Feynman diagrams. We describe a novel way of calculating these amplitudes, motivated by a conjectured relation to twistor space, in which the problem of summing Feynman diagrams is replaced by the problem of solving a certain set of algebraic equations.

scholarly journals Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Tung Tran
Keyword(s):  
Twistor Space ◽  
The Self ◽  
Yang Mills ◽  
Penrose Transform ◽  
Flat Background ◽  
Straightforward Generalization ◽  
Higher Spin ◽  
Formula Type

Abstract We present the inverse Penrose transform (the map from spacetime to twistor space) for self-dual Yang-Mills (SDYM) and its higher-spin extensions on a flat background. The twistor action for the higher-spin extension of SDYM (HS-SDYM) is of $$ \mathcal{BF} $$ BF -type. By considering a deformation away from the self-dual sector of HS-SDYM, we discover a new action that describes a higher-spin extension of Yang-Mills theory (HS-YM). The twistor action for HS-YM is a straightforward generalization of the Yang-Mills one.

Linear field equations on self-dual spaces

1980 ◽  
Vol 370 (1741) ◽  
pp. 173-191 ◽  
Keyword(s):  
Dual Space ◽  
Twistor Space ◽  
Rest Mass ◽  
The Self ◽  
Sheaf Cohomology ◽  
Field Equations ◽  
Yang Mills ◽  
Linear Field ◽  
Elliptic Complex ◽  
Mass Field

In a Riemannian context, a description is given of the Penrose correspondence between solutions of the anti-self-dual zero rest-mass field equations in a self-dual Yang-Mills background on a self-dual space X, and the sheaf cohomology groups H 1 ( Z, OF ( n )), for n ≤ -2of its twistor space Z . The case n = - 2 is fundamental for the construction of instantons on Euclidean space. It is further shown how H 1 ( Z, OF (-1)) corresponds to solutions of the self-dual Dirac equation, and an interpretation for H 1 ( Z, OF ( n )), for n ≥ 0, is given in terms of the cohomology of an elliptic complex on X .

scholarly journals $$ \mathcal{N} $$ = 7 On-shell diagrams and supergravity amplitudes in momentum twistor space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Connor Armstrong ◽  
Joseph A. Farrow ◽  
Arthur E. Lipstein
Keyword(s):  
Scattering Amplitudes ◽  
Twistor Space ◽  
Tree Level ◽  
Yang Mills

Abstract We derive an on-shell diagram recursion for tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 7 supergravity. The diagrams are evaluated in terms of Grassmannian integrals and momentum twistors, generalising previous results of Hodges in momentum twistor space to non-MHV amplitudes. In particular, we recast five and six-point NMHV amplitudes in terms of $$ \mathcal{N} $$ N = 7 R-invariants analogous to those of $$ \mathcal{N} $$ N = 4 super-Yang-Mills, which makes cancellation of spurious poles more transparent. Above 5-points, this requires defining momentum twistors with respect to different orderings of the external momenta.

scholarly journals A deformation of twistor space and a chiral mass term inN= 4 super Yang-Mills Theory

2006 ◽  
Vol 2006 (03) ◽  
pp. 027-027 ◽  
Author(s):  
Dah-Wei Chiou ◽  
Ori J Ganor ◽  
Bom Soo Kim
Keyword(s):  
Twistor Space ◽  
Mass Term ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals The worldsheet dual of free super Yang-Mills in 4D

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Matthias R. Gaberdiel ◽  
Rajesh Gopakumar
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Twistor Space ◽  
Free Field ◽  
Spectral Flow ◽  
Yang Mills ◽  
Finite Set ◽  
Single Trace ◽  
Covariant Version ◽  
Gauge Conditions

Abstract The worldsheet string theory dual to free 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills theory was recently proposed in [1]. It is described by a free field sigma model on the twistor space of AdS5 × S5, and is a direct generalisation of the corresponding model for tensionless string theory on AdS3 × S3. As in the case of AdS3, the worldsheet theory contains spectrally flowed representations. We proposed in [1] that in each such sector only a finite set of generalised zero modes (‘wedge modes’) are physical. Here we show that after imposing the appropriate residual gauge conditions, this worldsheet description reproduces precisely the spectrum of the planar gauge theory. Specifically, the states in the sector with w units of spectral flow match with single trace operators built out of w super Yang-Mills fields (‘letters’). The resulting physical picture is a covariant version of the BMN light-cone string, now with a finite number of twistorial string bit constituents of an essentially topological worldsheet.

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