Heterotic horizons and AdS$_3$ backgrounds that preserve 6 supersymmetries

TL;DR

This paper classifies heterotic horizons with 6 supersymmetries, showing their spatial sections are limited to specific topologies, and proves no such AdS3 backgrounds exist under certain conditions.

Contribution

It provides a topological classification of heterotic horizons with 6 supersymmetries and demonstrates the non-existence of corresponding AdS3 solutions with these properties.

Findings

Heterotic horizons with 6 supersymmetries have spatial sections diffeomorphic to SU(3) or S^2×S^3×SO(3).

No heterotic AdS3 solutions with 6 supersymmetries exist under the assumed conditions.

Re-examination of conditions for 4 supersymmetries reveals similarities with compact Calabi-Yau manifolds with torsion.

Abstract

We prove, under suitable global assumptions, that the only heterotic horizons with closed 3-form field strength that preserve strictly 6 supersymmetries have spatial horizon section diffeomorphic to either $SU(3)$ or $S^2\times S^3\times SO(3)$, up to identifications with the action of a discrete group. Under similar assumptions, which include the compactness of the transverse space, we demonstrate that there are no heterotic AdS$_3$ solutions that preserve 6 supersymmetries. The proof is based on a topological argument. We also re-examine the conditions required for the existence of such backgrounds that preserve 4 supersymmetries focusing on those that admit an additional $\oplus^2\mathfrak{u}(1)$ symmetry. We provide some additional explanation for the existence of solutions and point out the similarities that these conditions have with those that have recently emerged in the classification of compact strong 6-dimensional Calabi-Yau manifolds with torsion.