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High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
Інший ID:
2010 Mathematics Subject Classification: 81T30; 83E30
DOI: http://dx.doi.org/10.3842/SIGMA.2012.045
DOI: http://dx.doi.org/10.3842/SIGMA.2012.045
Посилання:
High-Energy String Scattering Amplitudes and Signless Stirling Number Identity / J. Lee, C.H. Yan, Y. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 29 назв. — англ.
Підтримка:
We thank Rong-Shing Chang, Song He, Yoshihiro Mitsuka and Keijiro Takahashi for helpful
discussions. This work is supported in part by the National Science Council, 50 billions project of Ministry of Education and National Center for Theoretical Science, Taiwan.
Дата:
2012
Переглядів:
487
Завантажень:
210
Анотація:
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.
