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arXiv · hep-th/0507146

Current Correlators and AdS/CFT Geometry

Edwin Barnes·Elie Gorbatov·Ken Intriligator·Jason Wright
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Abstract

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, $τ_{RR}$ of its two-point function. We show that the geometric Z-minimization condition of Martelli, Sparks, and Yau precisely implements $τ_{RR}$ 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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Edwin Barnes, Elie Gorbatov, Ken Intriligator, Jason Wright. 2005-07-14. Current Correlators and AdS/CFT Geometry. https://doi.org/10.1016/j.nuclphysb.2005.10.013

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