$W_3$ string scattering

TL;DR

This paper extends the group theoretic method to calculate tree level scattering amplitudes in $W_3$ strings, revealing the necessity of additional states linked to the Ising model's energy operator.

Contribution

It introduces a formalism incorporating background charge fields into $W_3$ string scattering calculations, connecting string amplitudes with Ising model correlations.

Findings

Scattering amplitudes involve Ising model correlation functions

Additional states with intercept 1/2 are required in the spectrum

Four tachyon amplitude analysis supports new spectrum states

Abstract

The group theoretic method is extended to include fields with a background charge. This formalism is used to compute the tree level scattering for $W_3$ strings. The scattering amplitudes involve Ising model correlation functions. A detailed study of the four tachyon amplitude shows that the $W_3$ string must possess additional states in its spectrum associated with intercept $1/2$ and the energy operator of the Ising model.