Introduction to the Ads/CFT Correspondence

15 January 2016

By Horaţiu Năstase
Cambridge University Press


The aim of this book is to give a pedagogical introduction to Anti-de Sitter/Conformal Field Theory, or AdS/CFT, which is the relation between quantum field theory with conformal invariance, living in our flat 4D space, and string theory, which is a quantum theory of gravity and other fields, living in the background solution of AdS5 × S5 (5D anti-de Sitter space multiplied by a five-sphere).

Assuming knowledge of only the basics of quantum field theory, the text provides readers with all of the concepts and tools needed to engage with AdS/CFT. In the first part, the author describes some fundamental concepts of general relativity, supersymmetry, supergravity, string theory, conformal field theory and D-branes. He has chosen not to overload the text with too many details about these fields, to keep the reader focused. The second section provides a clear and rigorous dissertation on AdS/CFT correspondence (in the context of its best understood example). Finally, in the third part, more specialised applications are discussed, such as QCD, quark–gluon plasma and condensed matter.

The book is self-contained, introducing all of the necessary basic concepts and most of the AdS/CFT methods and tools, but for an in-depth or exhaustive treatment, the reader is advised to refer to research articles. The many examples and exercises at the end of each chapter reveal the pedagogical vocation of the volume, nevertheless it will also be a useful reference for researchers in the fields of particle, nuclear and condensed-matter physics.

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