The AdS/CFT Correspondence

Ideas, techniques, and results concerning

the N=4 super-Yang-Mills theory and its deformations.

November 9 - November 23

Institut Henri Poincare

Daniel Z. Freedman (MIT/LPTENS/IHP))

The content of IHP Lecture notes 37 can be found in

FIELD THEORY INSIGHT FROM THE AdS/CFT CORRESPONDENCE by D. Freedman and P. Henry-Labordere

hep-th/0011086

A more detailed and complete review of the AdS/CFT correspondence can be found in

SUPERSYMMETRIC GAUGE THEORIES AND THE AdS/CFT CORRESPONDENCE (TASI 2001 Lecture notes) by Eric D'Hoker and Daniel Z. Freedman

hep-th/0201253

Lecture 1 BASIC IDEAS AND COMPUTATION OF 2- AND 3-POINT CORRELATION FUNCTIONS

• Review of the boundary (N=4 SYM) and bulk (D=10,IIB supergravity) theories.

• Geometries and isometries of Euclidean AdS_d+1. The inversion isometry.

• The AdS/CFT prescription for correlation functions

• The computation of 2- and 3-point correlators.

• Non-renormalization theorems

• Extremal correlators

Lecture 2 4-POINT FUNCTIONS IN CFT_4 AND FROM AdS/CFT

• Implications of conformal symmetry

• The operator product expansion

• Single and double trace operators

• AdS/CFT diagrams for 4-point functions

• Bulk-to-bulk propagators for scalars, gauge bosons, and gravitons

• Computing exchange diagrams

• Asymptotics and the operator product expansion.

• Extracting anomalous dimensions of double trace operators

Lecture 3 RENORMALIZATION GROUP FLOWS FROM AdS/CFT

(Details to be announced)