Current Correlators and AdS/CFT Geometry

Details Current Correlators and AdS/CFT Geometry Current Correlators and AdS/CFT Geometry

2005-07-14

arxiv.org/abs/hep-th/0507146v1

Nucl.Phys.B732:89-117,2006

Physics

High Energy Physics

High Energy Physics - Theory

37 pages

Scientific paper

10.1016/j.nuclphysb.2005.10.013

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.

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