Introduction to the AdS/CFT Correspondence

Providing a pedagogical introduction to the rapidly developing field of AdS/CFT correspondence, this is one of the first texts to provide an accessible introduction to all the necessary concepts needed to engage with the methods, tools and applications of AdS/CFT. Without assuming anything beyond an introductory course in quantum field theory, it begins by guiding the reader through the basic concepts of field theory and gauge theory, general relativity, supersymmetry, supergravity, string theory and conformal field theory, before moving on to give a clear and rigorous account of AdS/CFT correspondence. The final section discusses the more specialised applications, including QCD, quark-gluon plasma and condensed matter. This book is self-contained and learner-focused, featuring numerous exercises and examples. It is essential reading for both students and researchers across the fields of particle, nuclear and condensed matter physics.

Table of Contents

Part I. Background

1. Elements of Quantum Field Theory and Gauge Theory

2. Basics of General Relativity. Anti-de Sitter Space

3. Basics of Supersymmetry

4. Basics of Supergravity

5. Kaluza-Klein Reduction

6. Black Holes and p-Branes

7. String Theory Actions and Spectra

8. Elements of Conformal Field Theory

9. D-Branes

Part II. Basics of AdS/CFT for N=4 SYM vs AdS5xS5

10. The AdS/CFT Correspondence: Motivation, Definition, and Spectra

11. Witten Prescription and 3-Point Correlator Calculations

12. Holography in Lorentzian Signature: Poincare and Global Coordinates

13. Solitonic Objects in AdS/CFT

14. Quarks and the Wilson Loop

15. Finite Temperature and N=4 SYM Plasmas

16. Scattering Processes and Gravitational Shockwave Limit

17. The pp Wave Correspondence

18. The Heisenberg XXX Spin Chain Hamiltonian H_{XXX}

Part Ill. AdS/CFT Developments and Gauge-Gravity Dualities

19. Other Conformal Cases

20. The 3-Dimensional ABJM Model vs AdS4xCP3

21. Gravity Duals

22. Holographic Renormalization

23. RG Flow Between Fixed Points

24. Phenomenological Gauge-Gravity Duality I: AdS/QCD

25. Phenomenological Gauge-Gravity Duality II: AdS/CMT

26. Gluon Scattering: the Alday-Maldacena Prescription

27. Holographic Entanglement Entropy: the Ryu-Takayanagi Prescription

Review

“A remarkably comprehensive introduction to an important subject, which should be accessible to those with some basic background in quantum field theory and general relativity.”

Michael Dine, University of California, Santa Cruz

“Horaƫiu Năstase has managed to capture both the depth and breadth of the gauge/gravity duality in a wonderfully pedagogical manner. I can very well see Introduction to the AdS/CFT Correspondence becoming a standard reference for both graduate students as well as seasoned researchers in the field.”

Jeff Murugan, University of Cape Town

“A welcome survey of what has become a broad and well-established area of research … a useful reference for students entering the field as well as for experienced practitioners, both in string theory and in other communities.”

Diego Trancanelli, University of São Paulo

‘A pedagogical book on this sophisticated and rapidly developing subject is clearly welcome. Horaţiu Năstase’s very readable Introduction to the AdS/CFT Correspondence is such a book. Written by a well-known expert on the AdS/CFT correspondence and its applications, the book is intended for graduate students and researchers who want to be acquainted with the new holographic techniques. … many details presented by Năstase are not available in existing books … [The] book is written in a student-friendly style with detailed explanations and many worked-out calculations. Each chapter ends with a summary of important concepts and a set of exercises. It will certainly be of great help both to those teaching an advanced graduate course on the AdS/CFT correspondence and to students or researchers planning to learn it by themselves. Introduction to AdS/CFT Correspondence is a valuable addition to the small set of existing books on the topic.’ Alfonso V. Ramallo, Physics Today

Book Description

A pedagogical and self-contained introduction to AdS/CFT correspondence aimed at graduate students and researchers across theoretical physics.

About the Author

Horaţiu Năstase is a Researcher at the Institute for Theoretical Physics at the State University of São Paulo, Brazil. To date, his career has spanned four continents. As an undergraduate he studied at the University of Bucharest and Copenhagen University. He later completed his PhD at the State University of New York, Stony Brook, before moving to the Institute for Advanced Study, Princeton, where his collaboration with David Berenstein and Juan Maldacena defined the pp-wave correspondence. He has also held research and teaching positions at Brown University and the Tokyo Institute of Technology.