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 SIGMA, 2012, Volume 8, 045, 9 pages (Mi sigma722)

High-energy string scattering amplitudes and signless Stirling number identity

Jen-Chi Leea, Catherine H. Yanb, Yi Yanga

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

Abstract: 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.

Keywords: string scattering amplitudes, stirling number identity.

DOI: https://doi.org/10.3842/SIGMA.2012.045

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ArXiv: 1012.5225
MSC: 81T30; 83E30
Received: April 23, 2012; in final form July 10, 2012; Published online July 18, 2012
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Citation: Jen-Chi Lee, Catherine H. Yan, Yi Yang, “High-energy string scattering amplitudes and signless Stirling number identity”, SIGMA, 8 (2012), 045, 9 pp.

Citation in format AMSBIB
\Bibitem{LeeYanYan12} \by Jen-Chi Lee, Catherine H. Yan, Yi Yang \paper High-energy string scattering amplitudes and signless Stirling number identity \jour SIGMA \yr 2012 \vol 8 \papernumber 045 \totalpages 9 \mathnet{http://mi.mathnet.ru/sigma722} \crossref{https://doi.org/10.3842/SIGMA.2012.045} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2958985} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306612200001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864854252} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. He S., Lee J.-Ch., Yang Y., “Exponential Fall-Off Behavior of Regge Scatterings in Compactified Open String Theory”, Prog. Theor. Phys., 128:5 (2012), 887–901
2. Fu Ch.-H., Lee J.-Ch., Tan Ch.-I., Yang Y., “Recurrence Relations of Higher Spin Bpst Vertex Operators for Open Strings”, Phys. Rev. D, 88:4 (2013), 046004
3. Lee J.-Ch., Mitsuka Y., “Recurrence Relations of Kummer Functions and Regge String Scattering Amplitudes”, J. High Energy Phys., 2013, no. 4, 082
4. Lai Sh.-H., Lee J.-Ch., Yang Y., “The Lauricella functions and exact string scattering amplitudes”, J. High Energy Phys., 2016, no. 11, 062
5. Sh.-H. Lai, J.-Ch. Lee, T. Lee, Y. Yang, “Solving Lauricella string scattering amplitudes through recurrence relations”, J. High Energy Phys., 2017, no. 9, 130
6. Y. Yang, “Symmetry of string scattering amplitudes”, XXIV International Conference on Integrable Systems and Quantum Symmetries (ISQS-24), Journal of Physics Conference Series, 804, IOP Publishing Ltd, 2017, UNSP 012043
7. Lai Sh.-H., Lee J.-Ch., Yang Y., “The Sl(K+3, C) Symmetry of the Bosonic String Scattering Amplitudes”, Nucl. Phys. B, 941 (2019), 53–71
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