Heterotic horizons and AdS3 backgrounds that preserve 6 supersymmetries

A bstract 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 either to SU (3) or to S 2 × S 3 × 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 $$ {\oplus}^2\mathbf{\mathfrak{u}}(1) $$ ⊕ 2 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.