On Minisuperspace Models of S-branes

In this note we reconsider the minisuperspace toy models for rolling and bouncing tachyons. We show that the theories require to choose boundary conditions at infinity since particles in an exponentially unbounded potential fall to infinity in finite world-sheet time. Using standard techniques from operator theory, we determine the possible boundary conditions and we compute the corresponding energy spectra and minisuperspace 3-point functions. Based on this analysis we argue in particular that world-sheet models of S-branes possess a discrete spectrum of conformal weights containing both positive and negative values. Finally, some suggestions are made for possible relations with previous studies of the minisuperspace theory.