Geometry and supersymmetry of heterotic warped flux AdS backgrounds

Abstract

Abstract: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 AdS n backgrounds with n = 3. Moreover the warp factor of AdS 3 backgrounds is constant, the geometry is a product AdS 3 × M 7 and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of M 7 has been specified in all cases. For 2 supersymmetries, it has been found that M 7 admits a suitably restricted G 2 structure. For 4 supersymmetries, M 7 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, M 7 has an SU(2) structure and can be described locally as a S 3 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.

Anomaly corrected heterotic horizons

“…For the global analysis, we shall assume that the spatial cross-section of the event horizon is smooth and compact, without boundary, and that all near-horizon fields are also smooth. As a result of this analysis, we find that there are no AdS 2 solutions (at zero and first order in α ′ ) to heterotic supergravity, which completes the classification of heterotic AdS solutions in [33]. We also show that all of the conditions of supersymmetry reduce to a pair of gravitino KSEs and a pair of algebraic KSEs on the spatial…”

“…Such Lichnerowicz type theorems have been established for near-horizon geometries in D=11 supergravity [9], type IIB [10] and type IIA supergravity (both massive and massless) [11,12], as well as for AdS geometries in ten and eleven dimensional supergravity [33,[37][38][39].…”

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

“…2 See [27][28][29][30][31][32] for discussions on the classification of this type of heterotic and M theory vacua.…”

All superalgebras for warped AdS 2 and black hole near horizon geometries

“…In this case, the Ricci tensor of S vanishes which is a contradiction as S 8 has a non-vanishing Ricci tensor. Also there are no near horizon geometries with non-trivial fluxes and AdS 2 backgrounds in heterotic supergravity that preserve more than 8 supersymmetries [23].…”