The Lauricella Functions and Exact String Scattering Amplitudes

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.

20 pages, no figure, extended form of arXiv:1603.00396

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Cited by in corpus (10)

• Deformation of the Cubic Open String Field Theory
• New Series Representations for the Two-Loop Massive Sunset Diagram
• Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge
• Covariant Open String Field Theory on Multiple $Dp$-Branes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry
• The exact SL(K+3,C) symmetry of string theory
• Comment on "High Energy Symmetry of String Theory"
• Residues of bosonic string scattering amplitudes and the Lauricella functions
• The stringy scaling loop expansion and stringy scaling violation