Arbitrary Four String Scattering at High Energy and Fixed Angle

TL;DR

This paper computes high-energy, fixed-angle scattering amplitudes for arbitrary open and closed bosonic strings using a group theoretic approach, revealing simplified multi-string vertices at tree and one loop levels and proposing a general all-loops form.

Contribution

It introduces a simplified form of multi-string vertices at high energy and fixed angle, extending to all loops with a path integral derivation, and compares with prior results.

Findings

Simplified multi-string vertices at high energy and fixed angle

Agreement with Gross and Mende for tachyon scattering

Differences in scattering amplitudes for other string states

Abstract

We calculate, using the group theoretic approach to string theory, the tree and one loop scattering of four open and closed arbitrary bosonic string states. In the limit of high energy, but fixed angle, the multi-string vertex at tree and one loop levels that we find takes a very simple form. We propose, and present arguments for, a form for the high energy multi-string vertex at all loops; in particular we give a path integral derivation of this vertex. Our results agree with those of Gross and Mende for tachyon scattering amplitudes, but those for any other string scattering are substantially different from that discussed in reference [5]. We also develop some of the technology used in the group theoretic method to compute loop corrections.