Coaction and double-copy properties of configuration-space integrals at genus zero

Understand

We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory.

• For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction.
• We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension $\alpha'$ or the dimensional-regularization parameter $\epsilon$ of Feynman integrals.
• Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures.