On minisuperspace models of S-branes

In this note we reconsider the minisuperspace toy models for rolling andbouncing tachyons. We show that the theories require to choose boundaryconditions at infinity since particles in an exponentially unbounded potentialfall to infinity in finite world-sheet time. Using standard techniques fromoperator theory, we determine the possible boundary conditions and we computethe corresponding energy spectra and minisuperspace 3-point functions. Based onthis analysis we argue in particular that world-sheet models of S-branespossess a discrete spectrum of conformal weights containing both positive andnegative values. Finally, some suggestions are made for possible relations withprevious studies of the minisuperspace theory.Comment: 24 pages, 3 figure