# Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

@article{Cachazo2014ScatteringEA, title={Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM}, author={Freddy Cachazo and Song He and Ellis Ye Yuan}, journal={Journal of High Energy Physics}, year={2014}, volume={2015}, pages={1-43} }

A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1)M . The second operation turns gravitons into gluons and we call it…

## 436 Citations

### Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

- Physics
- 2017

A bstractUsing the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with…

### Einstein-Yang-Mills from pure Yang-Mills amplitudes

- Physics
- 2016

A bstractWe present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations…

### One-loop amplitudes in Einstein-Yang-Mills from forward limits

- Physics
- 2022

We present a method to compute the integrands of one-loop Einstein-Yang-Mills amplitudes for any number of external gauge and gravity multiplets. Our construction relies on the double-copy structure…

### Scattering equations in AdS: scalar correlators in arbitrary dimensions

- MathematicsJournal of High Energy Physics
- 2020

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula…

### Chiral splitting and N = 4 Einstein-Yang-Mills tree amplitudes in 4d

- Mathematics
- 2017

: We present a world-sheet formula for all tree level scattering amplitudes, in all trace sectors, of four dimensional N ≤ 4 supersymmetric Einstein-Yang-Mills theory, based on the reﬁned scattering…

### One-loop amplitudes on the Riemann sphere

- Mathematics
- 2015

A bstractThe scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for…

### Gluons and gravitons at one loop from ambitwistor strings

- Physics
- 2017

A bstractWe present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results…

### Conformal Gravity from Gauge Theory

- Physics
- 2017

We use the duality between color and kinematics to obtain scattering amplitudes in non-minimal conformal N=0,1,2,4 (super)gravity theories. Generic tree amplitudes can be constructed from a double…

### Gluons and gravitons at one loop from ambitwistor strings

- PhysicsJournal of High Energy Physics
- 2018

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the…

### New formulas for amplitudes from higher-dimensional operators

- Mathematics
- 2016

A bstractIn this paper we study tree-level amplitudes from higher-dimensional operators, including F3 operator of gauge theory, and R2, R3 operators of gravity, in the Cachazo-He-Yuan formulation. As…

## References

SHOWING 1-10 OF 54 REFERENCES

### Einstein-Yang-Mills scattering amplitudes from scattering equations

- Mathematics
- 2014

A bstractWe present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for…

### Scattering amplitudes in N = 2 Maxwell-Einstein and Yang-Mills / Einstein supergravity

- Physics
- 2015

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The…

### Scattering in three dimensions from rational maps

- Mathematics
- 2013

A bstractThe complete tree-level S-matrix of four dimensional $ \mathcal{N}=4 $ super Yang-Mills and $ \mathcal{N}=8 $ supergravity has compact forms as integrals over the moduli space of certain…

### Ambitwistor strings and the scattering equations at one loop

- Physics
- 2014

A bstractAmbitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of…

### Scattering of massless particles in arbitrary dimensions.

- MathematicsPhysical review letters
- 2014

A compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions is presented and Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.

### On the tree level S matrix of Yang-Mills theory

- Physics
- 2004

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of…

### Scattering amplitudes in N=2$$ \mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

- Physics
- 2014

A bstractWe expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2$$ \mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four…

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

- Physics
- 2008

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…

### A 'Twistor String' Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA

- Mathematics
- 2012

We propose a new formulation of the complete tree-level S-matrix of N = 8 supergravity. The new formula for n particles in the k R-charge sector is an integral over the Grassmannian G(2,n) and uses…