Density of States and Tachyons in Open and Closed String Theory

In this note we reexamine the possibility of constructing stable non-supersymmetric theories that exhibit an exponential density of states. For weakly coupled closed strings there is a general theorem, according to which stable theories with an exponential density of states must exhibit an almost exact cancellation of spacetime bosons and fermions (not necessarily level by level). We extend this result to open strings by showing that if the above cancellation between bosons and fermions does not occur, the open strings do not decouple from a closed string tachyon even in the NCOS scaling limit. We conclude with a brief comment on the proposed generalization of the AdS/CFT correspondence to non-supersymmetric theories.