  We propose a closed string tachyon action including kinetic and potential
terms for non-supersymmetric orbifolds. The action is given in terms of
solutions to $tt^*$ equations which captures the geometry of vacua of the
corresponding N=2 worldsheet theory. In certain cases the solutions are well
studied. In case of tachyons of ${\bf C}/Z_n$, solutions to affine toda
equations determine the action. We study the particular case of ${\bf C}/Z_3\to
{\bf C}$ in detail and find that the Tachyon action is determined in terms of a
solution to Painleve III equation.
