Skip to Content

Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers

We set up a tree-level six point scattering process in which two strings are separated longitudinally such that they could only interact directly via the non-local spreading effect predicted by light cone gauge calculations and the Gross-Mende saddle point.  One string, the  `detector',  is produced at a finite time with energy $E$ by an auxiliary $2\to 2$ sub-process, with kinematics such that it has sufficient resolution to detect the longitudinal spreading of an additional incoming string, the `source'. We test this hypothesis, and find that in this regime, the amplitude exhibits support over the predicted longitudinal separation of order $\alpha'E$, with its peak support shifted early by this amount.
In an appropriate kinematic regime, the worldsheet OPE leads to a factorized Regge form for the amplitude which precisely corresponds to the decomposition into the auxilliary four-point process and the detector-source scattering.  We support this interpretation by showing that the size of the amplitude is inconsistent with other interactions between the incoming strings, that the effect is robust against deformations that preserve the predicted spreading, and that the amplitude degrades as predicted when deformed so that the resolution of the detector string is reduced.   We contrast this with the behavior of tree-level quantum field theory with similar kinematics.  This provides a direct manifestation of the scale of longitudinal spreading in a gauge-invariant S-matrix amplitude, in a calculable process with significant amplitude which simulates the dynamics of time-translated horizon infallers.