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Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

Department of Electrophysics, National Chiao-Tung University, Hsinchu 300, Taiwan
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Symmetry 2019, 11(8), 1045; https://doi.org/10.3390/sym11081045
Received: 18 June 2019 / Revised: 15 July 2019 / Accepted: 2 August 2019 / Published: 13 August 2019
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Abstract

In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory. View Full-Text
Keywords: symmetries of strings; hard string scattering amplitudes; regge string scattering amplitudes; high energy limits; zero norm states; linear relations; recurrence relations symmetries of strings; hard string scattering amplitudes; regge string scattering amplitudes; high energy limits; zero norm states; linear relations; recurrence relations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lee, J.-C.; Yang, Y. Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory. Symmetry 2019, 11, 1045.

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