The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes

TL;DR

This paper reveals that bosonic string scattering amplitudes can be described using the SL(K+3,C) symmetry group, enabling a unified solution and providing a proof for Gross conjecture in the high-energy limit.

Contribution

The authors identify an SL(K+3,C) symmetry underlying string scattering amplitudes and develop a group-theoretic method to solve and relate these amplitudes, advancing the understanding of string symmetries.

Findings

Expressed SSA in terms of SL(K+3,C) basis functions.

Derived recurrence relations matching the Lie algebra structure.

Proved Gross conjecture using the SL(K+3,C) symmetry.

Abstract

We discover that the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was previously corrected and proved by the method of decoupling of zero norm states [4-10].