# The S-matrix in twistor space

@article{ArkaniHamed2009TheSI, title={The S-matrix in twistor space}, author={Nima Arkani-Hamed and Freddy Cachazo and Clifford Cheung and Jared Kaplan}, journal={Journal of High Energy Physics}, year={2009}, volume={2010}, pages={1-48} }

The marvelous simplicity and remarkable hidden symmetries recently uncovered in (Super) Yang-Mills and (Super)Gravity scattering amplitudes strongly suggests the existence of a “weak-weak” dual formulation of these theories where these structures are made more manifest at the expense of manifest locality. In this note we suggest that in four dimensions, this dual description lives in (2, 2) signature and is naturally formulated in twistor space. We begin at tree-level, by recasting the momentum…

## 163 Citations

Dual superconformal invariance, momentum twistors and Grassmannians

- Physics
- 2009

Dual superconformal invariance has recently emerged as a hidden symmetry of planar scattering amplitudes in = 4 super Yang-Mills theory. This symmetry can be made manifest by expressing amplitudes in…

Maximally helicity-violating diagrams in twistor space and the twistor action

- Physics
- 2012

MHV diagrams give an efficient Feynman diagram-like formalism for calculating gauge theory scattering amplitudes on momentum space. Although they arise as the Feynman diagrams from an action on…

Scattering amplitudes and Wilson loops in twistor space

- Mathematics
- 2011

This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for super-Yang–Mills. Wilson loops and amplitudes are derived from first principles using…

Scattering amplitudes and BCFW recursion in twistor space

- Mathematics
- 2009

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering…

MHV diagrams in twistor space and the twistor action

- Physics
- 2011

MHV diagrams give an efficient Feynman diagram-like formalism for calculating gauge theory scattering amplitudes on momentum space. Although they arise as the Feynman diagrams from an action on…

CHY Formulae and Soft Theorems in N=4 Super Yang-Mills Theory

- Mathematics
- 2017

The study of scattering amplitudes in quantum field theories (QFTs) is equally important for high energy phenomenology and for theoretical understanding of fundamental physics. Over the last 15 years…

Twistor theory at fifty: from contour integrals to twistor strings

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

The Newtonian limit of twistor theory is discussed and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function is discussed.

Gravity in Twistor Space and its Grassmannian Formulation

- Mathematics
- 2014

We prove the formula for the complete tree-level S-matrix of N = 8 super- gravity recently conjectured by two of the authors. The proof proceeds by showing that the new formula satisfies the same…

Supersymmetric Yang-Mills and supergravity amplitudes at one loop

- Physics
- 2009

By applying the known expressions for super Yang-Mills (SYM) and supergravity (SUGRA) tree amplitudes, we write generating functions for the next-to-next-to-maximally helicity violating (NNMHV) box…

Twistor Theory as an Approach to Fundamental Physics

- Mathematics
- 2018

The original motivations underlying the introduction of twistor theory are described, demanding a (3+1)-dimensional space-time theory dependent upon complex analysis and geometry. Space-time points…

## References

SHOWING 1-10 OF 117 REFERENCES

Scattering amplitudes and BCFW recursion in twistor space

- Mathematics
- 2009

Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering…

Twistor quantisation and curved space-time

- Physics
- 1968

AbstractThe formalism of twistors [the ‘spinors’ for the group O(2,4)] is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1,…

Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

- Physics, Mathematics
- 2010

Twistor actions for non-self-dual fields; a new foundation for twistor-string theory

- Physics
- 2005

Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a…

A Note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

- Mathematics, Physics
- 2008

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S matrix of the maximally…

Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

- Mathematics
- 2007

We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence…

Einstein Supergravity and New Twistor String Theories

- Physics
- 2006

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second…

On tree amplitudes in gauge theory and gravity

- Physics
- 2008

The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in…