String Theory, Misaligned Supersymmetry, and the Supertrace Constraints

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We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints Str(M⁰)=0 and Str(M²)=Λat tree level, where Λis 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 thus severely constrain the possible supersymmetry-breaking scenarios in string theory, and suggest a new intrinsically stringy mechanism whereby such supertrace constraints may be satisfied without phenomenologically unacceptable consequences.