Abstract
We investigate chaotic dynamics in tree-level S-matrices describing the scattering of tachyons, photons and gravitons on highly excited open and closed bosonic strings, motivated by the string/black hole complementarity. The eigenphase spacing distribution and other indicators of quantum chaotic scattering suggest that the dynamics is only weakly chaotic, consisting of both regular/Poisson and chaotic/Wigner-Dyson processes. Only for special values of momenta and (for photon scattering) scattering angles do we find strong chaos of random matrix type. These special values correspond to a crossover between two regimes of scattering, dominated by short versus long partitions of the total occupation number of the highly excited string; they also maximize the information entropy of the S-matrix. The lack of strong chaos suggests that perturbative dynamics of highly excited strings can never describe the universal properties and maximal chaos of black hole horizons.
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Acknowledgments
We are grateful to Matthew Dodelson, David Berenstein and Dmitry Ageev for stimulating discussions. The authors acknowledge funding provided by the Institute of Physics Belgrade, through the grant by Ministry of Science, Technological Development, and Innovations of the Republic of Serbia. M. Č. would like to acknowledge the Steklov Mathematical Institute (Moscow), International Center for Theoretical Physics (Trieste) and Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (Project ID 39083149) for hospitality and the opportunity to present and discuss this work.
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Savić, N., Čubrović, M. Weak chaos and mixed dynamics in the string S-matrix. J. High Energ. Phys. 2024, 101 (2024). https://doi.org/10.1007/JHEP03(2024)101
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DOI: https://doi.org/10.1007/JHEP03(2024)101