Loop Integrands for Scattering Amplitudes from the Riemann Sphere.

Author: 

Geyer, Y
Mason, L
Monteiro, R
Tourkine, P

Publication Date: 

16 September 2015

Journal: 

Physical review letters

Last Updated: 

2019-08-16T03:53:16.19+01:00

Issue: 

12

Volume: 

115

DOI: 

10.1103/physrevlett.115.121603

page: 

121603-

abstract: 

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 depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.

Symplectic id: 

568619

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article