Generalized $\W_3$ Strings from Free Fields

TL;DR

This paper investigates the possibility of new generalized W_3 string theories through alternative quantization methods, but finds no evidence of consistent new models, especially ruling out critical strings based on magic realizations.

Contribution

It introduces a general framework for constructing W_3-like strings without relying on quantum W_3 algebra, and demonstrates the non-existence of new consistent theories within this approach.

Findings

No new consistent W_3-like string theories found.

Critical strings based on magic realizations are ruled out.

Provides conditions for the existence of W_3-like strings.

Abstract

The conventional quantization of w_3 strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W_3 string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W_3 algebra. We study W_3-like strings with a direct spacetime interpretation---that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w_3 algebra. We give the general conditions for the existence of W_3-like strings, and comment how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.