Loop Integrands for Scattering Amplitudes from the Riemann Sphere.

@article{Geyer2015LoopIF,
  title={Loop Integrands for Scattering Amplitudes from the Riemann Sphere.},
  author={Yvonne Geyer and Lionel Mason and Ricardo Monteiro and Piotr Tourkine},
  journal={Physical review letters},
  year={2015},
  volume={115 12},
  pages={
          121603
        }
}
The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that… 

Figures from this paper

One-loop amplitudes on the Riemann sphere

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

Two-loop scattering amplitudes from ambitwistor strings: from genus two to the nodal Riemann sphere

A bstractWe derive from ambitwistor strings new formulae for two-loop scattering amplitudes in supergravity and super-Yang-Mills theory, with any number of particles. We start by constructing a

Cosmological scattering equations at tree-level and one-loop

Abstract We recently proposed a formula for tree-level n-point correlators of massive ϕ4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and

Gluons and gravitons at one loop from ambitwistor strings

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

Superstring Loop Amplitudes from the Field Theory Limit

We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit. We focus on the type II

Two-loop scattering amplitudes: double-forward limit and colour-kinematics duality

Abstract We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward

Space-time CFTs from the Riemann sphere

A bstractWe consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space — the natural setting for

Cosmological Scattering Equations

We propose a worldsheet formula for the computation of tree-level correlation functions of a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model

New worldsheet formulae for conformal supergravity amplitudes

A bstractWe use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet

New formulas for amplitudes from higher-dimensional operators

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 10 REFERENCES

JHEP 1504

  • 013
  • 2015

JHEP 1404

  • 104
  • 2014

and E

  • Y. Yuan, Phys.Rev.Lett. 113, 171601
  • 2014

and E

  • Y. Yuan,
  • 2014

and H

  • Johansson, Phys.Rev. D78, 085011
  • 2008

JHEP 1505

  • 120
  • 2015

and K

  • A. Roehrig,
  • 2015

JHEP 1405

  • 010
  • 2014

and H

  • Johansson, Phys.Rev.Lett. 105, 061602
  • 2010

JHEP 1407

  • 048
  • 2014