String Theory, Misaligned Supersymmetry, and the Supertrace Constraints

TL;DR

This paper shows that string theory in four dimensions enforces supertrace constraints on the spectrum, linking them to the cosmological constant, and introduces a hidden 'misaligned supersymmetry' mechanism that constrains supersymmetry breaking.

Contribution

It demonstrates that string consistency naturally leads to supertrace constraints and introduces the concept of misaligned supersymmetry as a new mechanism for supersymmetry breaking.

Findings

Supertrace constraints are satisfied at tree level in string theories.

Misaligned supersymmetry explains supertrace constraints without full spacetime supersymmetry.

Constraints limit possible supersymmetry-breaking scenarios in string theory.

Abstract

We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints Str(M^0)=0 and Str(M^2)=\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 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.