String theory, misaligned supersymmetry, and the supertrace constraints.

Abstract

We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints $\mathrm{Str}1\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and $\mathrm{Str}{M}^{2}\ensuremath{\propto}\ensuremath{\Lambda}$ at tree level, where $\ensuremath{\Lambda}$ 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.