The Exact SL(K+3,C) Symmetry of 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 conjectured by Gross [1-3] and proved in [4-9] in the hard scattering limit, the recurrence relations in the Regge scattering limit [14-16] and the extended recurrence relations in the nonrelativistic scattering limit [19] discovered recently. Finally, as an application, we calculate a new recurrence relation of SSA which is valid for all energies.