Kummer function and High energy String Scatterings

Abstract

Based on a summation algorithm for Stirling number identity developed recently, we discover that the ratios calculated previously among high energy string scattering amplitudes in the Gross regime (GR) can be extracted from the Kummer function of the second kind. This function naturally shows up in the leading order of high energy string scattering amplitudes in the Regge regime (RR). As a result, the identity suggested by string theory calculation can be rigorously proved by a totally different but sophisticated mathematical method. We conjecture and give evidences that the existence of these ratios in the RR persists to all orders in the Regge expansion of high energy string scattering amplitudes.

8 pages. v2:9 pages,Eq.(14) was rigorous proved,Eqs added and 1 ref added. v3:typos corrected. v5:11 pages, eqs and refs added

References in corpus (2)

• The Pomeron and Gauge/String Duality
• Patterns of High energy Massive String Scatterings in the Regge regime

Cited by in corpus (5)

• Review on High energy String Scattering Amplitudes and Symmetries of String Theory
• Regge Closed String Scattering and its Implication on Fixed angle Closed String Scattering
• High-Energy Symmetry of Bosonic Open String Theory in the Light-like Linear Dilaton Background
• Vertex Operators and Scattering Amplitudes of the Bosonic Open String Theory in the Linear Dilaton Background
• String Scattering Amplitudes in High Energy Limits