  We construct the second quantized action for sub-critical closed string field
theory with zero cosmological constant in dimensions $ 2 \leq D < 26$,
generalizing the non-polynomial closed string field theory action proposed by
the author and the Kyoto and MIT groups for $D = 26$. The proof of gauge
invariance is considerably complicated by the presence of the Liouville field
$\phi$ and the non-polynomial nature of the action. However, we explicitly show
that the polyhedral vertex functions obey BRST invariance to all orders. By
point splitting methods, we calculate the anomaly contribution due to the
Liouville field, and show in detail that it cancels only if $D - 26 + 1 + 3 Q ^
2 = 0 $, in both the bosonized and unbosonized polyhedral vertex functions. We
also show explicitly that the four point function generated by this action
reproduces the shifted Shapiro-Virasoro amplitude found from $c=1$ matrix
models and Liouville theory in two dimensions. LATEX file.
