Density of States and Tachyons in Open and Closed String Theory

TL;DR

This paper investigates the conditions under which non-supersymmetric string theories can have an exponential density of states, highlighting the necessity of boson-fermion cancellation and its implications for stability and tachyon decoupling.

Contribution

It extends the theorem on exponential density of states from closed to open strings, emphasizing the role of boson-fermion cancellation for stability.

Findings

Stable non-supersymmetric theories require near-exact boson-fermion cancellation.

Without cancellation, open strings remain coupled to closed string tachyons.

The results impact the understanding of non-supersymmetric AdS/CFT generalizations.

Abstract

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.