Recurrence relations of Kummer functions and Regge string scattering amplitudes

TL;DR

This paper uncovers an infinite set of recurrence relations among Regge string scattering amplitudes, enabling algebraic solutions for all such amplitudes in open bosonic string theory using Kummer functions.

Contribution

It introduces a novel approach based on recurrence relations and Kummer functions to analyze Regge string scattering amplitudes, bypassing zero-norm state decoupling.

Findings

All Regge string scattering amplitudes can be algebraically solved.

Recurrence relations are dual to high-energy fixed angle amplitude symmetries.

Method applies to arbitrary mass levels in open bosonic string theory.

Abstract

We discover an infinite number of recurrence relations among Regge string scattering amplitudes \cite{bosonic,RRsusy} of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.