Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications

Abstract

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.

27 pages; D=2 mistake corrected; typos fixed and references added

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• Flat equivariant gerbes: holonomies and dualities
• SW(3/2,2) subsymmetry in G${}_2$, Spin(7) and N=2 CFTs
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Deformed Shatashvili-Vafa algebra for superstrings on AdS${}_3\times {\mathcal{M}}_7$