Trivial Spectrum of Free 1+1 Light-Cone Strings

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.