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

@article{Chiodaroli2017ExplicitFF, title={Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy}, author={Marco Chiodaroli and Murat G{\"u}naydin and Henrik Johansson and Radu Roiban}, journal={Journal of High Energy Physics}, year={2017}, volume={2017}, pages={1-33} }

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 up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ3 theory. The construction outlined in this paper holds in general…

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## References

SHOWING 1-10 OF 89 REFERENCES

### 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…

### Spontaneously broken Yang-Mills-Einstein supergravities as double copies

- Physics
- 2015

A bstractColor/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we…

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

- Mathematics
- 2014

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…

### Expansion of Einstein-Yang-Mills amplitude

- Physics
- 2017

A bstractIn this paper, we study from various perspectives the expansion of tree level single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes. By…

### 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…

### Pure gravities via color-kinematics duality for fundamental matter

- Physics
- 2014

A bstractWe give a prescription for the computation of loop-level scattering amplitudes in pure Einstein gravity, and four-dimensional pure supergravities, using the color-kinematics duality.…

### Perturbative quantum gravity as a double copy of gauge theory.

- PhysicsPhysical review letters
- 2010

It is conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones.

### Amplitude relations in heterotic string theory and Einstein-Yang-Mills

- Physics
- 2016

A bstractWe present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge…

### Gravity as the Square of Gauge Theory

- Physics
- 2010

We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged…