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 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.