Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton

TL;DR

The paper studies the soft limit of tree-level NS-NS massless closed-string amplitudes, showing a factorization into soft and hard parts and decomposing the full amplitude into bosonic and supersymmetric components. It computes the soft expansion through subsubleading order and demonstrates that the dilaton soft theorem is universal with no alpha' corrections in any string theory, while the graviton soft theorem in superstring theory matches the field-theory result after cancellations between bosonic and SUSY contributions. The authors express the (n+1)-point amplitude as a soft operator acting on the n-point amplitude and extend the analysis to heterotic strings via gauge invariance, showing dilaton universality persists. These results indicate a underlying symmetry guiding the dilaton's soft behavior and reinforce the universality of soft theorems across string theories.

Abstract

We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the bosonic string. Differently from the bosonic string, the supersymmetric soft theorem for the graviton has no string corrections at subsubleading order. The dilaton soft theorem, on the other hand, is found to be universally free of string corrections in any string theory.