Geometry and supersymmetry of heterotic warped flux AdS backgrounds

We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no AdSn backgrounds with n ≠ 3. Moreover the warp factor of AdS3 backgrounds is constant, the geometry is a product AdS3 × M7 and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of M7 has been specified in all cases. For 2 supersymmetries, it has been found that M7 admits a suitably restricted G2 structure. For 4 supersymmetries, M7 has an SU(3) structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, M7 has an SU(2) structure and can be described locally as a S3 fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kähler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of α′ corrections.