Bootstrap Principle for the Spectrum and Scattering of Strings

Creators: Cheung, Clifford¹; Hillman, Aaron¹; Remmen, Grant N.²

1. California Institute of Technology
2. New York University

Abstract

We show that the Veneziano amplitude of string theory is the unique solution to an analytically solvable bootstrap problem. Uniqueness follows from two assumptions: faster than power-law falloff in high-energy scattering and the existence of some infinite sequence in momentum transfer at which higher-spin exchanges cancel. The string amplitude—including the mass spectrum—is an output of this bootstrap. If the amplitude merely vanishes at high energies, the solution is a three-parameter family containing the Veneziano, Coon, and hypergeometric amplitudes, and more.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Acknowledgement

We thank Nima Arkani-Hamed, Justin Berman, Henriette Elvang, David Gross, Sebastian Mizera, Hirosi Ooguri, Simon Telen, and Sasha Zhiboedov for discussions. C. C. and A. H. are supported by the Department of Energy (Grant No. DE-SC0011632) and by the Walter Burke Institute for Theoretical Physics. G. N. R. is supported by the James Arthur Postdoctoral Fellowship at New York University.

Funding

C. C. and A. H. are supported by the Department of Energy (Grant No. DE-SC0011632) and by the Walter Burke Institute for Theoretical Physics. G. N. R. is supported by the James Arthur Postdoctoral Fellowship at New York University.

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