Dr Daniele Angelo Farotti

Extreme near-horizon geometries in D = 11 supergravity preserving four su-persymmetries are classified. It is shown that the Killing spinors fall into three possible orbits, corresponding to pairs of spinors defined on the spatial cross-sections of the horizon which have isotropy groups SU(3), G 2 , or SU(4). In each case, the conditions on the geometry and the 4-form flux are determined. The integrability conditions obtained from the Killing spinor equations are also investigated.

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.

We classify all warped dS5 backgrounds in D = 11 supergravity with enhanced supersymmetry. We show that backgrounds preserving N = 16 supersymmetries consist of either a stack of M5 branes with transverse space $\mathbb{R}^5$, or a generalized M5-brane configuration with transverse space $\mathbb{R} \times N_4$, where N4 is a hyper-Kähler manifold and the M5-brane harmonic function is determined by a hyper-Kähler potential on N4. Moreover, we find that there are no backgrounds preserving exactly N = 24 supersymmetries. Backgrounds preserving N = 32 supersymmetries correspond to either $\mathbb{R}^{1,10}$ or $AdS_7\times S^4$.