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arXiv · 1609.06014

The Lauricella Functions and Exact String Scattering Amplitudes

Sheng-Hong Lai·Jen-Chi Lee·Yi Yang
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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 SL(K+3,C) 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 [1-3] and later corrected and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit with associated SL(5,C) symmetry [19-21] and the extended recurrence relations in the nonrelativistic scattering limit with associated SL(4,C) symmetry [24] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.

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Sheng-Hong Lai, Jen-Chi Lee, Yi Yang. 2016-09-20. The Lauricella Functions and Exact String Scattering Amplitudes. https://doi.org/10.1007/jhep11(2016)062

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