AdS geometry from CFT on a general conformally flat manifold

AdS/CFT correspondence and Geometry

In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic renormalization, with the radial coordinate playing the role of time. In this a...

The Geometry of AdS/CFT

The AdS/CFT conjecture states that to every such manifold (L, gL) there is a dual superconformal field theory in four dimensions. This may be thought of as living on the Penrose conformal boundary of anti–de Sitter space, in the usual way. The AdS/CFT correspondence then makes some remarkable connections between field theory and geometry, some of which I have uncovered over the last year or so....

The flat space S - matrix from the AdS / CFT correspondence ?

We investigate recovery of the bulk S-matrix from the AdS/CFT correspondence, at large radius. It was recently argued that some of the elements of the S-matrix might be read from CFT correlators, given a particular singularity structure of the latter, but leaving the question of more general S-matrix elements. Since in AdS/CFT, data must be specified on the boundary, we find certain limitations...

Compactification of a Class of Conformally Flat 4-manifold

Current Correlators and AdS/CFT Geometry

We consider current-current correlators in 4d N = 1 SCFTs, and also 3d N = 2 SCFTs, in connection with AdS/CFT geometry. The superconformal U(1)R symmetry of the SCFT has the distinguishing property that, among all possibilities, it minimizes the coefficient, τRR of its two-point function. We show that the geometric Z-minimization condition of Martelli, Sparks, and Yau precisely implements τRR ...