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 limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations. We discuss the relationship between the formulae for non-supersymmetric theories and the Neveu-Schwarz sector of the formulae for maximally supersymmetric theories, which can be derived from ambitwistor strings. An important property of the loop integrands is that they are expressed in a representation that includes linear-type propagators. This representation exhibits a loop-level version of the colour- kinematics duality, which follows directly from tree level via the double-forward limit.
Highlights
The worldsheet techniques that inspire our work originated in Witten’s twistor string [1] describing four-dimensional super-Yang-Mills theory, and in the corresponding ‘connected prescription’ to compute scattering amplitudes [2]
The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations
Tree-level scattering amplitudes for n massless particles are computed as integrals over the moduli space of punctured Riemann spheres, M0,n
Summary
We start by reviewing the Cachazo-He-Yuan (CHY) formulae for treelevel scattering amplitudes in Yang-Mills theory and gravity, and their connection to the Bern-Carrasco-Johansson (BCJ) colour-kinematics duality. We review the analogous construction for one-loop integrands, with an eye to its extension to two loops.
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