Level-one intercept bound in covariant string quantization ($a\le 1$)

A polarization obeys $p\cdot ϵ=0$ and $p^2=(a-1)/{\alpha }^{\prime }$. If $a>1$, spacelike momentum allows a negative-norm timelike polarization. Thus ghost absence requires $a\le 1$. At $a=1$ the null string state identification $ϵ\sim ϵ+\lambda p$ leaves $D-2$ polarizations.