Protostring Scattering Amplitudes

TL;DR

This paper computes tree-level scattering amplitudes for a generalized string model called the protostring, exploring its properties, special cases, and high-energy behavior, with a focus on its unique symmetry features compared to other string theories.

Contribution

It introduces a generalized protostring model with additional transverse fields, calculates explicit scattering amplitudes, and analyzes their symmetry and high-energy properties.

Findings

All amplitudes for open strings with no oscillator excitations are obtained.

Special cases like maximal helicity violation simplify the amplitudes.

The protostring has a unique Lorentz symmetry, differing from the bosonic string.

Abstract

We calculate some tree level scattering amplitudes for a generalization of the protostring, which is a novel string model implied by the simplest string bit models. These bit models produce a lightcone worldsheet which supports $s$ integer moded Grassmann fields. In the generalization we supplement this Grassmann worldsheet system with $d=24-s$ transverse coordinate worldsheet fields. The protostring corresponds to $s=24$ and the bosonic string to $s=0$. The interaction vertex is a simple overlap with no operator insertions at the break/join point. Assuming that $s$ is even we calculate the multi-string scattering amplitudes by bosonizing the Grassmann fields, each pair equivalent to one compactified bosonic field, and applying Mandelstam's interacting string formalism to a system of $s/2$ compactified and $d$ uncompactified bosonic worldsheet fields. We obtain all amplitudes for open strings with no oscillator excitations and for closed strings with no oscillator excitations and zero winding number. We then study in detail some simple special cases. Multi-string processes with maximal helicity violation have much simplified amplitudes. We also specialize to general four string amplitudes and discuss their high energy behavior. Most of these models are not covariant under the full Lorentz group $O(d+1,1)$. The exceptions are the bosonic string whose Lorentz group is $O(25,1)$ and the protostring whose Lorentz group is $O(1,1)$. The models in between only enjoy an $O(1,1)\times O(d)$ spacetime symmetry.