SUPERTRACES IN STRING THEORY

We demonstrate that the spectrum of any consistent string theory in $D$ dimensions must satisfy a number of supertrace constraints: $Str~M^{2n}=0$ for $0 \leq n < D/2-1$, integer $n$. These results hold 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. [Talk given by R.C.M. at Strings '95; to appear in Proceedings]