IIB black hole horizons with five-form flux and extended supersymmetry

Abstract

Abstract:We classify under some assumptions the IIB black hole horizons with 5-form flux preserving more than 2 supersymmetries. We find that the spatial horizon sections with non-vanishing flux preserving 4 supersymmetries are locally isometric either to S 1 ×S 3 ×T 4 or to S 1 × S 3 × K 3 and the associated near horizon geometries are locally isometric to AdS 3 × S 3 × T 4 and AdS 3 × S 3 × K 3 , respectively. The near horizon geometries preserving more than 4 supersymmetries are locally isometric to R 1,1 × T 8 .

Index theory and dynamical symmetry enhancement of M-horizons

“…Assuming that the required Lichnerowicz type theorems can be established relating the number of Killing spinors to zero modes of Dirac operators, one does not expect that the index of the Dirac operator vanishes on the even-dimensional horizon sections. However, the investigation of heterotic horizons and those of 6-dimensional supergravity in [28], [29] and [30] both find that those with non-trivial fluxes preserve an even number of supersymmetries and have an sl(2, R) invariance subalgebra, but also see [31], [32]. So there may be a generalization of our results to even-dimensional horizons.…”

Classification of Near-Horizon Geometries of Extremal Black Holes

“…The theory is invariant under 32 supersymmetries. A variety of results concerning the classification of supersymmetric nearhorizon geometries in this theory have been derived [102,101,103]. Certain explicit classification results are known for near-horizon geometries with just a 5-form flux preserving more than two supersymmetries, albeit under certain restrictive assumptions [101].…”

“…A variety of results concerning the classification of supersymmetric nearhorizon geometries in this theory have been derived [102,101,103]. Certain explicit classification results are known for near-horizon geometries with just a 5-form flux preserving more than two supersymmetries, albeit under certain restrictive assumptions [101]. More generally, the existence of one supersymmetry places rather weak geometric constraints on the horizon cross sections H: generically H may be any almost Hermitian spin c manifold [103].…”

Timelike structures of ten-dimensional supersymmetry

“…Instead of looking at a full black-hole solution, we restrict ourselves to the near horizon geometry which can be viewed as an AdS 2 × M 8 vacuum solution where M 8 is typically a fibration of a compact manifold M 6 over S 2 . Classifications of black hole horizons in a similar spirit were given in [48,49].…”