Soft Theorems in Superstring Theory
Ashoke Sen
TL;DR
The paper proves the subleading soft graviton theorem for tree-level amplitudes in heterotic and type II string theories with NS/NSNS external states and one soft graviton, and establishes the leading soft graviton theorem for multiple soft gravitons. Using a background-independent, superstring field theory framework, the author shows that the soft-graviton contributions reduce to universal operators acting on the hard amplitude, with identical results to those known from field theory in the tree-level limit. The work extends to leading multi-soft cases and discusses generalizations to soft photons and all-orders (loop) extensions, while highlighting subtleties from Riemann-tensor terms and Ramond-sector states. Together, these results connect string-theory amplitudes to universal soft theorems and point to paths for proving subleading soft graviton behavior beyond tree level.
Abstract
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum field theories coupled to gravity with generic interactions. We discuss the technical issue involved in extending this analysis to loop amplitudes of superstring theory including Ramond sector external states, and its possible resolution.