Residues of bosonic string scattering amplitudes and the Lauricella functions

TL;DR

This paper explicitly calculates residues of n-point string scattering amplitudes and shows they can be expressed using Lauricella functions, revealing an exact SL(K+3,C) symmetry in open bosonic string theory.

Contribution

It introduces a method to compute residues of all SSA using on-shell recursion and expresses these residues with Lauricella functions, highlighting a new symmetry.

Findings

Residues of all SSA can be expressed via Lauricella functions.

The residues exhibit an exact SL(K+3,C) symmetry.

An iteration relation among residues suggests potential to soften hard SSA.

Abstract

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.