Discrete States in the $W_3$ String

TL;DR

This paper constructs the low-lying discrete states of the two-scalar $W_3$ string, revealing infinite towers of states and analogues to ground ring generators, advancing understanding of its spectrum.

Contribution

It introduces a method to identify discrete states in the $W_3$ string, including states analogous to ground ring generators, expanding the known spectrum.

Findings

Identification of low-lying discrete states

Existence of infinite towers of discrete states

States analogous to ground ring generators

Abstract

We construct the low-lying discrete states of the two-scalar $W_3$ string. This includes states that correspond to the analogues of the ground ring generators of the ordinary two-dimensional string. These give rise to infinite towers of discrete states at higher levels.