Long-range nonlocality in six-point string scattering: Simulation of black hole infallers

Abstract

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 a non-local spreading effect such as that 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 → 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 in a gauge-invariant S-matrix calculation convolved with an appropriate wavepacket peaked at a separation X between the central trajectories of the source and produced detector. The amplitude exhibits support for scattering at the predicted longitudinal separation X ∼ α E, in sharp contrast to the analogous quantum field theory amplitude (whose support manifestly traces out a tail of the position-space wavefunction). The effect arises in a regime in which the string amplitude is not obtained as a convergent sum of such QFT amplitudes, and has larger amplitude than similar QFT models (with the same auxiliary four point amplitude). In a linear dilaton background, the amplitude depends on the string coupling as expected if the scattering is not simply occuring on the wavepacket tail in string theory. This manifests the scale of longitudinal spreading in a gauge-invariant S-matrix amplitude, in a calculable process with significant amplitude. It simulates a key feature of the dynamics of time-translated horizon infallers.

Varying dilaton as a tracer of classical string interactions

“…As discussed in [1], this interaction is parametrically stronger than appropriate tree-level quantum field theory models with the same kinematics and wavepackets. Still, the assessment of whether the interaction may occur on the tail of the wavepackets can be subtle, and it is useful to probe that in a different way.…”

“…One interesting application of a varying dilaton is to help diagnose the level of nonlocality in string interactions [1,6,7,8]. In this section we determine the effect of the linear dilaton on string spreading in light cone gauge [6].…”

“…In this section, we applied it to straightforward string oscillations as a test of the method. It is interesting to apply this to help trace out the level of non-locality in string interactions [1].…”

“…In this section, we add a linear dilaton to the six point S-matrix amplitude considered in [1], a process which exhibits the predicted longitudinal spreading scale as a function of the separation between the central positions of a string and putative detector of its spreading, at the peak of their wavepackets. As discussed in [1], this interaction is parametrically stronger than appropriate tree-level quantum field theory models with the same kinematics and wavepackets.…”

“…This case is simple enough to be tractable, while more generic than string theory in Minkowski spacetime. It has various applications, including some relevant in horizon physics such as [1,2]. For example, for a generic total dimensionality D > D crit , the simplest classical solution of the theory is a runaway to weak coupling along a timelike linear dilaton trajectory, corresponding to the rolling scalar solution sourced by a positive scalar potential.…”