Spinorial geometry, horizons and superconformal symmetry in six dimensions

摘要

The spinorial geometry method of solving Killing spinor equations is reviewedas it applies to 6-dimensional (1,0) supergravity. In particular, it isexplained how the method is used to identify both the fractions ofsupersymmetry preserved by and the geometry of all supersymmetric backgrounds.Then two applications are described to systems that exhibit superconformalsymmetry. The first is the proof that some 6-dimensional black hole horizonsare locally isometric to $AdS_3\times \Sigma^3$, where $\Sigma^3$ isdiffeomeorphic to $S^3$. The second one is a description of all supersymmetricsolutions of 6-dimensional (1,0) superconformal theories and in particular oftheir brane solitons.