Abstract
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.
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Lai, SH., Lee, JC. & Yang, Y. The Lauricella functions and exact string scattering amplitudes. J. High Energ. Phys. 2016, 62 (2016). https://doi.org/10.1007/JHEP11(2016)062
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DOI: https://doi.org/10.1007/JHEP11(2016)062