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 [He S., Lee J.C., Yang Y., 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.
|期刊||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|出版狀態||Published - 1 十二月 2012|