A Very Introductory AdS/CFT

The AdS/CFT correspondence, conjectured by Maldecena in late 1997, has been playing an essential role in modern string theory. The original version of this gravity/gauge AdS/CFT correspondence states an equivalence between Type 2B string theory on AdS5 × S and N = 4 super Yang-Mills theory in 4D, under certain parameter region. Namely, for these two theories, the operator variables, physical states, correlation functions and dynamics, are equivalent to one another. In this elementary-level note, we briefly discuss the geometry of AdS space, and show that the isometry group of AdSd+1 is isomorphic to the conformal group of the flat Minkowski space R1,d−1, which motivates theAdS/CFT . Then we will provide a precise statement of theAdS/CFT correspondence. We mainly follow the expositions of following references: 1. Aharony, O., Gubser, S.S., Maldacena, J., Ooguri, H. and Oz, Y., 2000. Large N field theories, string theory and gravity. Physics Reports, 323(3), pp.183-386. ArXiv: 9905111. 2. D’Hoker, Eric, and Daniel Z. Freedman. ”Supersymmetric gauge theories and the AdS/CFT correspondence.” ArXiv:0201253v2.