Chaotic scattering of highly excited strings

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.

arXiv comment65 pages, 11 figures; published version

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• Classical Limit of Higher-Spin String Amplitudes
• Chaos bound and its violation in charged Kiselev black hole
• Chaos in a many-string scattering amplitude
• Scattering Massive String Resonances through Field-Theory Methods
• Measure for chaotic scattering amplitudes
• Non-Lorentzian Chaos and Cosmological Holography
• Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
• Chaos in the Quantum Field Theory $S$-matrix
• Photon emission from an excited string
• Evaluating one-loop string amplitudes
• Transient chaos analysis of string scattering
• The chaotic emergence of thermalization in highly excited string decays
• Homoclinic RG flows, or when relevant operators become irrelevant
• Chaos Bound and its violation in Black p-brane
• Weak chaos and mixed dynamics in the string S-matrix
• String Thermodynamics In and Out of Equilibrium: Boltzmann Equations and Random Walks
• Chaotic RG Flow in Tensor Models
• From locality to irregularity: Introducing local quenches in massive scalar field theory
• Chaotic instability in the BFSS matrix model
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• Chaotic and Thermal Aspects in the Highly Excited String S-Matrix
• Deterministic Chaos vs Integrable Models
• String amplitudes and mutual information in confining backgrounds: the partonic behavior
• Scattering and Strebel graphs
• Non-Negativity of BMN Two-Point Functions With Three String Modes
• From Confinement to Chaos in AdS/CFT Correspondence via Non-equilibrium Local States
• Maximally Chaotic Dynamical System of Infinite Dimensionality
• Classical string profile for a class of DDF amplitudes