The covariant scattering and cohomology of $W_3$ strings

TL;DR

This paper develops a covariant formalism for $W_3$ string scattering, utilizing screening charges and cohomology to identify physical states, and demonstrates that the constructed amplitudes align with known Ising model correlations.

Contribution

It introduces a covariant scattering formalism for $W_3$ strings using screening charges and cohomology, revealing an infinite set of states generated from a few basic ones.

Findings

Scattering amplitudes include Ising model correlation functions.

An infinite number of cohomology states are generated from three basic states.

The formalism aligns with previous results on $W_3$ string scattering.

Abstract

A general formalism for covariant $W_3$ string scattering is given. It is found necessary to use screening charges that are constructed from the $W_3$ fields including ghosts. The scattering amplitudes so constructed contain within them Ising model correlation functions and agree with those found previously by the authors. Using the screening charge and a picture changing operator, an infinite number of states in the cohomology of Q are generated from only three states. We conjecture that, apart from discrete states, these are all the states in the cohomology of Q.