Subleading Soft Factor for String Disk Amplitudes

TL;DR

This paper proves that the subleading soft factor for tree-level open-string disk amplitudes has no α' corrections and matches the field-theory (Yang-Mills) form. By analyzing generalized Euler integrals in the soft expansion and employing a careful integral approximation, the authors establish the universal S^(1) structure for arbitrary N with explicit 4- and 5-point checks. They then discuss extending these results to closed strings via KLT, suggesting pathways through CHY-like formulations and highlighting remaining questions for higher-order soft factors. Overall, the work reinforces the universality of soft theorems in string theory and clarifies how open-string results inform closed-string gravity amplitudes.

Abstract

We investigate the behavior of superstring disk scattering amplitudes in the presence of a soft external momentum at finite string tension. We prove that there are no $α'$-corrections to the field theory form of the subleading soft factor $S^{(1)}$. At the end of this work, we also comment on the possibility to find the corresponding subleading soft factors in closed string theory using our result and the KLT relations.