Trivial Spectrum of Free 1+1 Light-Cone Strings

TL;DR

This paper demonstrates that the BRST cohomology of free 1+1 light-cone strings is trivial, containing only the tachyon and excluding all excited states, highlighting potential issues with this gauge choice.

Contribution

It reveals that the BRST cohomology in the free light-cone gauge is trivial, contrasting with other gauges and models, and raises questions about the gauge's consistency.

Findings

Only the two-dimensional tachyon remains in the cohomology.

All excited states are excluded at a fundamental level.

Potential problems with the light-cone gauge choice are suggested.

Abstract

The BRST cohomology of 1+1 strings in a free light-cone gauge contains only the two-dimensional tachyon, and excludes all excited states of both matter and ghosts, including the special states that arise in the continuum conformal gauge quantization and in the $c = 1$ matrix models. This exclusion takes place at a very basic level, and therefore may signal some serious problems or at least unresolved issues involved in this gauge choice.