Current Correlators and AdS/CFT Geometry

Abstract

We consider current-current correlators in 4d $\mathbb{N}=1$ SCFTs, and also 3d $\mathbb{N}=2$ 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.

37 pages

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Cited by in corpus (31)

• An Index for 4 dimensional Super Conformal Theories
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• On the Time Dependence of Holographic Complexity
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Supersymmetric Field Theories on Three-Manifolds
• Exactly Marginal Deformations and Global Symmetries
• Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity
• Supersymmetric AdS_5 Solutions of Type IIB Supergravity
• Weak Gravity Conjecture in AdS/CFT
• Five-dimensional Supergravity Dual of a-Maximization
• From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
• Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
• On RG Flow of tau_{RR} for Supersymmetric Field Theories in Three-Dimensions
• Deformations of Toric Singularities and Fractional Branes
• Comments on a-maximization from gauged supergravity
• Comments on Anomalies and Charges of Toric-Quiver Duals
• The exceptional generalised geometry of supersymmetric AdS flux backgrounds
• Betti multiplets, flows across dimensions and c-extremization
• Are tiny gauge couplings out of the Swampland?
• Compact Conformal Manifolds
• Broken current anomalous dimensions, conformal manifolds and RG flows
• Free Yang-Mills vs. Toric Sasaki-Einstein
• 3D ${\tau }_{RR}$-minimization in AdS${}_4$ gauged supergravity
• Half BPS states in AdS_5 x Y^{p,q}
• Higgsing and Superpotential Deformations of ADE Superconformal Theories
• Equivalence of A-Maximization and Volume Minimization
• Triangle Anomalies from Einstein Manifolds
• Kerr-Newman black holes from $\mathcal{N}=1^{\ast }$
• ${\tau }_{RR}$ minimization in presence of hypermultiplets
• Supersymmetric Adler Functions and Holography
• Universal Cardy-Like Behavior of 3D Partition Functions from Supersymmetric Localization