Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 045, 9 pages      arXiv:1012.5225

High-Energy String Scattering Amplitudes and Signless Stirling Number Identity

Jen-Chi Lee a, Catherine H. Yan b and Yi Yang a
a) Department of Electrophysics, National Chiao-Tung University, Hsinchu, Taiwan, R.O.C.
b) Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

Received April 23, 2012, in final form July 10, 2012; Published online July 18, 2012

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.

Key words: string scattering amplitudes; stirling number identity.

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