String Theory, Misaligned Supersymmetry, and the Supertrace Constraints

We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints $\mathrm{Str}1=0\mathrm{}$ and $\mathrm{Str}{M}^2\propto \Lambda$ at tree level, where $\Lambda$ is the one-loop string cosmological constant. This result holds for a large class of string theories, including critical heterotic strings. For strings lacking spacetime supersymmetry, these supertrace constraints will be satisfied as a consequence of a hidden “misaligned supersymmetry” in the string spectrum. These results suggest a new intrinsically stringy mechanism whereby such supertrace constraints may be satisfied without phenomenologically unacceptable consequences.