A Note on Soft Factors for Closed String Scattering

TL;DR

This paper demonstrates that closed string graviton tree amplitudes satisfy the same subleading soft theorem as field-theory gravity by leveraging three ingredients: the subleading soft behavior of open-string disk amplitudes, the single-valued projection of multiple zeta values, and the KLT relations linking open and closed string amplitudes. It extends the open-string results to heterotic and other string theories via sv, and shows that, through an appropriate basis transformation and the KLT kernel, the closed-string subleading soft factor S^{(1)}_{ m g} matches the field-theory result in any dimension. While the leading soft behavior reproduces Weinberg’s factor, the subleading term requires nontrivial kernel identities, and a fully field-theory-proof of the subsubleading term remains open. Overall, the work strengthens the connection between string and field theory soft theorems and highlights a dimension-independent route to deriving gravitational soft behavior from open-string data.

Abstract

In this note, it is shown that closed string graviton scattering amplitudes obey the same subleading soft limit as field theory graviton scattering amplitudes. The result is derived using a combination of recent results and methods including the subleading soft expansion for type I open string gluon disk scattering amplitudes, the single value projection for multiple $ζ$ values, and the KLT relations in field and string theory.