Supersymmetric AdS/CFT and black holes

AdS/CFT对应关系是反德西特时空中弦/ m理论与共形场论的对偶关系。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。我们的目标是在超对称的背景下进一步理解AdS/CFT，并探索由此产生的新的几何结构。一个目标将是获得新的见解来推导超对称AdS黑洞类的熵。我们将通过IIB型超引力的超对称AdS3解、d=2超对称共形场论的对偶以及d= 11超引力的超对称AdS2解提供一个丰富的框架，这些超引力是超对称黑洞解的近视界极限。在这两种情况下，都有一个奇维紧凑的内部流形支持GK几何。D3膜和M2膜包裹紧实的二维表面，还有一个有趣的子类由二维轨道组成，称为纺锤。为了获得对AdS对应的新见解，我们将对这些主题进行研究。

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.