On the Spectrum and Scattering of W_3 Strings

TL;DR

This paper investigates scattering processes in W_3 string theory, revealing new physical states, analyzing amplitude properties, and proposing a simplified formalism to better understand the theory's unitarity and structure.

Contribution

It introduces a new formalism involving ghost-matter field mixing that simplifies the physical state structure in W_3 string theory.

Findings

Discovery of new physical states with continuous momentum

Evidence supporting unitarity despite complex ghost structure

A simplified formalism for studying W_3 strings

Abstract

We present a detailed investigation of scattering processes in $W_3$ string theory. We discover further physical states with continuous momentum, which involve excitations of the ghosts as well as the matter, and use them to gain a better understanding of the interacting theory. The scattering amplitudes display factorisation properties, with states from the different sectors of the theory being exchanged in the various intermediate channels. We find strong evidence for the unitarity of the theory, despite the unusual ghost structure of some of the physical states. Finally, we show that by performing a transformation of the quantum fields that involves mixing the ghost fields with one of the matter fields, the structure of the physical states is dramatically simplified. The new formalism provides a concise framework within which to study the $W_3$ string.