Universality in string interactions

TL;DR

This paper addresses the universality of the leading transcendental coefficients in the $\alpha'$-expansion of tree-level string amplitudes across open and closed string theories. It shows that by expressing the bosonic open-string integrand in the same disk-integral basis as the open superstring and using $\alpha'$-dependent but rational kinematic factors, the leading transcendental terms match the superstring; closed strings follow via the KLT relations. The authors provide explicit checks up to seven points and outline an all-multiplicity extension in a companion paper, supported by BCJ/KK relations and IBP reductions. The results imply universal coefficients in the low-energy effective actions and offer a framework for organizing tree-level amplitudes across string theories and potentially for gravity counterterms.

Abstract

In this letter, we provide evidence for universality in the low-energy expansion of tree-level string interactions. More precisely, in the alpha'-expansion of tree-level scattering amplitudes, we conjecture that the leading transcendental coefficient at each order in alpha' is universal for all perturbative string theories. We have checked this universality up to seven points and trace its origin to the ability to restructure the disk integrals of open bosonic string into those of the superstring. The accompanying kinematic functions have the same low-energy limit and do not introduce any transcendental numbers in their alpha'-corrections. Universality in the closed-string sector then follows from the KLT-relations.