Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications

TL;DR

This paper explores the constraints and realizations of spacetime supersymmetry in low-dimensional heterotic string compactifications, revealing that three-dimensional cases align with supergravity, while two-dimensional cases exhibit more exotic structures.

Contribution

It provides a detailed analysis of worldsheet structures associated with spacetime supersymmetries in low-dimensional heterotic string vacua, including new insights into two-dimensional exotic possibilities.

Findings

Three-dimensional vacua correspond to supergravity compactifications.

Two-dimensional vacua include more exotic, less understood structures.

The analysis clarifies the relationship between worldsheet theories and spacetime supersymmetry.

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.