Abstract
The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal N = 2 supersymmetry is obtained. A supersymmetric near-horizon solution is constructed which is a U(1) fibration of AdS 3 over a particular Aloff–Wallach space. It is proven that this solution preserves the conditions required for N = 2 supersymmetry, but does not satisfy the necessary condition required for further supersymmetry enhancement. Hence, there exist supersymmetric near-horizon heterotic solutions preserving exactly N = 2 supersymmetry.
Highlights
The geometric properties of horizons of supersymmetric black holes are very closely linked to the notion of supersymmetry enhancement
By exploiting certain similarities between heterotic supergravity and N = 2, D = 5 supergravity, this near-horizon supersymmetry doubling was proven to hold for heterotic horizons in [3], utilizing the classification of supersymmetric heterotic solutions in [4, 5]
We have found that there exists a near-horizon solution of heterotic supergravity preserving exactly N = 2 supersymmetry, utilizing the family of G2 structures constructed in [21]
Summary
The geometric properties of horizons of supersymmetric black holes are very closely linked to the notion of supersymmetry enhancement. We proceed to construct an explicit near-horizon geometry, which is a U(1) fibration of AdS3 over a certain 7-dimensional Aloff-Wallach space Mk,l = SU (3)/U (1)k,l equipped with co-closed G2 structure This solution satisfies the conditions required for N = 2 supersymmetry, but fails to satisfy the condition which is necessary and sufficient for further supersymmetry enhancement. This solution is an example of a “descendant” solution, for which the gravitino equation holds for all the spinors, but the dilatino equation does not hold for two of the spinors [12, 13] This establishes the existence of exactly N = 2 supersymmetric heterotic near-horizon geometries. In Appendix C, properties of the Fernandez-Gray [14] classification of G2 structures are listed
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