Journal of High Energy Physics

, 2016:62 | Cite as

The Lauricella functions and exact string scattering amplitudes

  • Sheng-Hong Lai
  • Jen-Chi Lee
  • Yi YangEmail author
Open Access
Regular Article - Theoretical Physics


We discover that the 26D open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state can be expressed in terms of the D-type Lauricella functions with associated \( \mathrm{S}\mathrm{L}\left(K+3,\mathbb{C}\right) \) symmetry. As a result, SSA and symmetries or relations among SSA of different string states at various limits calculated previously can be rederived. These include the linear relations first conjectured by Gross [1-5] and later corrected and proved in [6-12] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated \( \mathrm{S}\mathrm{L}\left(5,\mathbb{C}\right) \) symmetry [24-26] and the extended recurrence relations in the nonrelativistic scattering limit with associated \( \mathrm{S}\mathrm{L}\left(4,\mathbb{C}\right) \) symmetry [29] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.


Bosonic Strings Higher Spin Symmetry 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of ElectrophysicsNational Chiao Tung UniversityHsinchuROC

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