Introduction to AdS/CFT Duality
时间： 每周三09:50-12:15, 2019-9-11 ~ 12-25
These lectures introduce basic aspects of the holographic duality between a quantum system on the D+1 dimensional bulk and its dual system on the D dimensional boundary. The fascinating gauge/gravity duality, and its mathematical and practical perspectives, is the main example. Gauge theory and string theory are two different theories defined in different ways, yet they have an equivalence in a nontrivial way. We describe the ‘t Hooft large N expansion in large N gauge theories. We then discuss Anti de Sitter Space/Conformal Field Theory correspondence and the GKPW relation. The three-point correlation functions relating to the amplitudes on the gravity will be discussed. Aspects of holography duality on Wilson loops, renormalization groups, QCD, Einstein manifolds, topological strings, AdS3 and AdS2, black holes, tensor networks, entanglement, and quantum computation will be discussed in details. The Penrose limit of AdS space, the plane-wave geometries, the BMN correspondence, and field theory operators with large scaling dimensions will also be discussed. The roles and aspects of permutation, Schur-Weyl duality, and nonplanarity in gauge theory and string theory will also be addressed.