= Solution
Take $D$ embedding coordinates and give one coordinate the background charge $q$. The remaining $D-1$ free bosons contribute $D-1$, while the distinguished coordinate contributes $1+6\alpha'q^2$, so the matter <central charge> is
$$
c_{\rm matter}=D+6\alpha'q^2.
$$
The <worldsheet ghost field>[worldsheet ghosts] contributes $-26$. Cancellation of the <worldsheet Weyl anomaly> therefore requires
$$
\boxed{q^2=\frac{26-D}{6\alpha'}},
$$
which is real for $D<26$ and produces a noncritical bosonic string.
In target-space language the <dilaton> is linear in this coordinate, so the local <string coupling> $g_s=e^\Phi$ changes exponentially. One end of the target direction is weakly coupled and the other is strongly coupled. Consequently <string perturbation theory> is trustworthy only in the weak-coupling region, rather than throughout the full background.
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