The Appell Function $F_1$ and Regge String Scattering Amplitudes

Abstract

We show that each 26D open bosonic Regge string scattering amplitude (RSSA) can be expressed in terms of one single Appell function $F_1$ in the Regge limit. This result enables us to derive infinite number of recurrence relations among RSSA at arbitrary mass levels, which are conjectured to be related to the known SL(5,C) dynamical symmetry of $F_1$. In addition, we show that these recurrence relations in the Regge limit can be systematically solved so that all RSSA can be expressed in terms of one amplitude. All these results are dual to high energy symmetries of fixed angle string scattering amplitudes discovered previously [4-8].

12 pages,no figure

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• Review on High energy String Scattering Amplitudes and Symmetries of String Theory
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• The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry
• The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes