The $W_3$-string spectrum

TL;DR

This paper analyzes the spectrum of $W_3$ strings, revealing a constrained scalar field and a unitary theory with a massive graviton, differing from standard string theories.

Contribution

It demonstrates how the $W_3$ string spectrum is affected by specific constraints, leading to a unique, consistent theory with a frozen scalar mode and a massive graviton.

Findings

Scalar field is frozen by the spin-3 constraint

Remaining theory is unitary and anomaly-free

The graviton becomes massive in the $W_3$ string context

Abstract

We study the spectrum of $W_3$ strings. In particular, we show that for appropriately chosen space-time signature, one of the scalar fields is singled out by the spin-3 constraint and is ``frozen'': no creation operators from it can appear in physical states and the corresponding momentum must assume a specific fixed value. The remaining theory is unitary and resembles an ordinary string theory in $d\ne26$ with anomalies cancelled by appropriate background charges. In the case of the $W_3$ string, however, the spin-two ``graviton'' is massive.