The exact SL(K+3,C) symmetry of string theory

TL;DR

This paper demonstrates that all open bosonic string scattering amplitudes can be expressed using Lauricella functions, revealing an exact SL(K+3,C) symmetry that extends previous results from four-point to all n-point amplitudes.

Contribution

It extends the known SL(K+3,C) symmetry from four-point to all n-point open bosonic string scattering amplitudes using on-shell recursion relations.

Findings

All SSA can be expressed in terms of Lauricella functions.

The symmetry enables solving all SSA with a single amplitude.

It reveals iteration relations and linear relations among SSA.

Abstract

By using on-shell recursion relation of string scattering amplitudes (SSA), we show that all n-point SSA of the open bosonic string theory can be expressed in terms of the Lauricella functions. This result extends the previous exact SL(K+3,C) symmetry of the 4-point Lauricella SSA (LSSA) of three tachyons and one arbitrary string states to the whole tree-level open bosonic string theory. Moreover, we present three applications of the SL(K+3,C) symmetry on the SSA. They are the solvability of all SSA in terms of one amplitude, the existence of iteration relations among residues of a given SSA so as to soften its hard scattering behavior and finally the re-derivation of infinite linear relations among hard SSA [12].