Residues of bosonic string scattering amplitudes and the Lauricella functions

Sheng-Hong Lai^1*, Jen-Chi Lee¹, Yi Yang¹

¹Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan

* Presenter:Sheng-Hong Lai, email:xgcj944137@gmail.com

We calculate explicitly residues of all n-point Koba-Nielsen (KN) amplitudes by using on-shell
recursion relation of string scattering amplitudes (SSA). In addition, we show that the residues of
all SSA including the KN amplitudes can be expressed in terms of the Lauricella functions. This
result demonstrates the exact SL(K + 3, C) symmetry of the tree-level open bosonic string theory.
Moreover, we derive an iteration relation among the residues of a given SSA. This iteration relation
is related to the SL(K + 3, C) symmetry and can presumably be used to soften the well-known
hard SSA.

Keywords: string theory, scattering , Lauricella functions, BCFW, n-point KN amplitudes