Chaotic scattering of highly excited strings

TL;DR

This paper investigates the chaotic behavior in scattering amplitudes involving highly excited strings, revealing complex structures and erratic dependencies indicative of chaos, through high-energy calculations and saddle-point analysis.

Contribution

It introduces a method to compute scattering amplitudes of excited strings and uncovers their chaotic properties at high energies and excitation levels.

Findings

Amplitudes are determined by saddle points in high-energy regimes.

Excited string scattering amplitudes exhibit erratic, chaotic behavior.

Derived a compact expression for excited string decay into two tachyons.

Abstract

Motivated by the desire to understand chaos in the $S$-matrix of string theory, we study tree level scattering amplitudes involving highly excited strings. While the amplitudes for scattering of light strings have been a hallmark of string theory since its early days, scattering of excited strings has been far less studied. Recent results on black hole chaos, combined with the correspondence principle between black holes and strings, suggest that the amplitudes have a rich structure. We review the procedure by which an excited string is formed by repeatedly scattering photons off of an initial tachyon (the DDF formalism). We compute the scattering amplitude of one arbitrary excited string and any number of tachyons in bosonic string theory. At high energies and high mass excited state these amplitudes are determined by a saddle-point in the integration over the positions of the string vertex operators on the sphere (or the upper half plane), thus yielding a generalization of the "scattering equations". We find a compact expression for the amplitude of an excited string decaying into two tachyons, and study its properties for a generic excited string. We find the amplitude is highly erratic as a function of both the precise excited string state and of the tachyon scattering angle relative to its polarization, a sign of chaos.