Supersymmetric AdS/CFT and black holes

ADS/CFT对应是反de-Sitter时空中的弦/M理论和共形场理论之间的对偶。它继续照亮我们对量子场论和量子引力的理解。此外，它还与有趣的几何结构有关。我们的主要目标是在超对称的背景下加深我们对ADS/CFT的理解，并探索出现的新的几何结构。一个目标将是在推导超对称ADS黑洞类的熵方面获得新的见解。作为超对称黑洞解的近视界极限，IIB型超重力超对称ADS_3解、对偶到d=2超对称共形场理论以及D=11超引力的超对称ADS_2解提供了一个丰富的框架。在这两种情况下，都存在一个奇维紧致内部流形，它支持GK几何。解可以来自D3膜和M2膜包裹紧的二维曲面，而一个有趣的子类由称为纺锤的二维旋转体组成。将对这些主题进行调查，以获得对ADS通信的新见解。

The AdS/CFT correspondence is a duality between string/M-theory in Anti-de-Sitter spacetime and conformal field theories. It continues to illuminate both our understanding of quantum field theory and of quantum gravity. Furthermore, it is associated with interesting geometric structures. The broad goals are to further our understanding of AdS/CFT in a supersymmetric context and explore the new geometric structures that arise. A goal will be to obtain new insights into deriving the entropy of classes of supersymmetric AdS black holes. A rich framework which will be explored, is provided by classes of supersymmetric AdS3 solutions of type IIB supergravity, dual to d=2 supersymmetric conformal field theories as well as supersymmetric AdS2 solutions of D=11 supergravity, which arise as the near horizon limit of supersymmetric black hole solutions. In both case there is an odd dimensional compact internal manifold which supports a GK geometry.The solutions can arise from D3 branes and M2 branes wrapping compact two dimensional surfaces and an interesting sub-class consists of two-dimensional orbifolds known as spindles. These topics will be investigated in order to obtain new insights into the AdS correspondence.