  We show that vanishing of the sigma-model beta-functions for the metric
$g_{\mu\nu}$, antisymmetric tensor $B_{\mu\nu}$ and dilaton $\Phi$ of any
string-theory model in $D$ dimensions at tree level can be obtained from a
universal effective action, provided that the field combination
$\sqrt{-g}e^{-2\Phi}$ is non-dynamical. The central-charge deficit term is
omitted from the action and appears as an integration constant at the level of
the field equations. The analysis is done at leading order in $\alpha'$, i.e.
at the two-derivative level in the effective description. It can be extended to
incorporate higher order string-loop corrections, Ramond-Ramond forms and
moduli fields. In all cases, the non-dynamical field combination turns out to
be $\sqrt{-g}\, U$, where $U$ is the effective potential. When certain fluxes
are fixed and the moduli fields are stabilized, no cosmological term will arise
in the action. Instead, the cosmological constant will appear as an integration
constant as in unimodular modifications of general relativity.
