×

High-energy string scattering amplitudes and signless Stirling number identity. (English) Zbl 1269.81139

Summary: We give a complete proof of a set of identities (7) proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values \(L\) rather than only for \(L=0\),1 proved previously. The identities for non-integer real value \(L\) were recently shown to be realized in high-energy compactified string scattering amplitudes [S. He et al., “Exponential fall-off behavior of Regge scatterings in compactified open string theory”, Prog. Theor. Phys. 128, No. 5, 887–901 (2012), arXiv:1012.3158]. The parameter \(L\) is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
81U05 \(2\)-body potential quantum scattering theory

Software:

Stirling
PDFBibTeX XMLCite
Full Text: DOI arXiv