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, tau(RR) of its two-point function. We show that the geometric Z-minimization condition of Martelli, Sparks, and Yau precisely implements tau(RR) minimization. This gives a physical proof that Z-minimization in geometry indeed correctly determines the superconformal R-charges of the field theory dual. We further discuss and compare current two point functions in field theory and AdS/CFT and the geometry of Sasaki-Einstein manifolds. Our analysis gives new quantitative checks of the AdS/CFT correspondence. (c) 2005 Published by Elsevier B.V.