Rolling tachyons from Liouville theory

In this work we propose an exact solution of the c = 1 Liouville model, i.e. of the world-sheet theory that describes the homogeneous decay of a closed string tachyon. Our expressions are obtained through careful extrapolation from the correlators of Liouville theory with c geq 25. In the c = 1 limit, we find two different theories which differ by the signature of Liouville field. The euclidean limit coincides with the interacting c = 1 theory that was constructed by Runkel and Watts as a limit of unitary minimal models. The couplings for the lorentzian limit are new. In contrast to the behavior at c>1, amplitudes in both c = 1 models are non-analytic in the momenta and consequently they are not related by Wick rotation.