The Appell Function $F_1$ and Regge String Scattering Amplitudes

TL;DR

This paper demonstrates that 26D open bosonic Regge string scattering amplitudes can be represented using a single Appell function F_1, leading to recurrence relations and a unified expression for all amplitudes, revealing underlying symmetries.

Contribution

It introduces a novel representation of Regge string scattering amplitudes using the Appell function F_1 and derives recurrence relations linking all amplitudes.

Findings

RSSA expressed via Appell function F_1

Infinite recurrence relations among RSSA

All amplitudes reducible to a single base amplitude

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].