Introduction to the AdS/CFT Correspondence

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.

Preface; Introduction; 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 dimensional 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 AdS5 × S5: 10. The AdS/CFT correspondence: motivation, definition and spectra; 11. Witten prescription and 3-point correlator calculations; 12. Holography in Lorentzian signature: Poincaré and global; 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. Spin chains; Part III. AdS/CFT Developments and Gauge-Gravity Dualities: 19. Other conformal cases; 20. The 3 dimensional ABJM model vs. AdS4 × CP3; 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.