The Low-level Spectrum of the $W_3$ String

TL;DR

This paper analyzes the spectrum of physical states in the $W_3$ string theory, revealing the massless photon state and exploring gauge symmetries through null states, up to specific excitation levels.

Contribution

It provides a detailed spectrum analysis of the $W_3$ string, including null states and gauge symmetries, at levels up to 2 and 4 for different scalar configurations.

Findings

The $W_3$ string has a photon as its only massless state.

Null physical states reveal gauge symmetries in the $W_3$ string.

Spectrum analyzed up to level 2 for multi-scalar and level 4 for two-scalar strings.

Abstract

We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.