Spacetime Supersymmetry in Low-Dimensional Perturbative Heterotic Compactifications

We study the constraints of spacetime supersymmetry for perturbative three- and two-dimensional Minkowski vacua of the critical heterotic string. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, we describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions we show that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification. As a recent orbifold construction shows, in two dimensions there are more exotic possibilities, and we discuss how these fit into our analysis. The constraints of spacetime supersymmetry for perturbative three- and two-dimensional Minkowski vacua of the critical heterotic string are investigated. Assuming a standard RNS construction of the spacetime supersymmetry generators and a compact unitary internal superconformal worldsheet theory, the authors describe the worldsheet structures associated to various spacetime supersymmetries. In three dimensions it is shown that there are no CFT surprises: each allowed spacetime supersymmetry is realized by a supergravity compactification.