  We compute, on the disk, the non-linear tachyon $\beta$-function, $\beta^T$,
of the open bosonic string theory. $\beta^T$ is determined both in an expansion
to the third power of the field and to all orders in derivatives and in an
expansion to any power of the tachyon field in the leading order in
derivatives. We construct the Witten-Shatashvili (WS) space-time effective
action $S$ and prove that it has a very simple universal form in terms of the
renormalized tachyon field and $\beta^T$. The expression for $S$ is well suited
to studying both processes that are far off-shell, such as tachyon
condensation, and close to the mass-shell, such as perturbative on-shell
amplitudes. We evaluate $S$ in a small derivative expansion, providing the
exact tachyon potential. The normalization of $S$ is fixed by requiring that
the field redefinition that maps $S$ into the tachyon effective action derived
from the cubic string field theory is regular on-shell. The normalization
factor is in precise agreement with the one required for verifying all the
conjectures on tachyon condensation. The coordinates in the space of couplings
in which the tachyon $\beta$-function is non linear are the most appropriate to
study RG fixed points that can be interpreted as solitons of $S$, $i.e.$
D-branes.
