Double-Trace Deformations of Conformal Correlations

Abstract

Large $N$ conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in $1/N$. This has a simple dual in AdS, where the flow is implemented by a change of boundary conditions, and provides a physical interpretation of single-valued conformal partial waves. We extract the change in the conformal dimensions and three-point coefficients of infinite families of double-trace composite operators. Some of these quantities are found to be sign-definite under double-trace flow. As an application, we derive anomalous dimensions of spinning double-trace operators comprised of non-singlet constituents in the $O(N)$ vector model.

29+15 pages. v2: typo corrected, minor changes in Appendix C

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• Holography from Conformal Field Theory
• Fractional M2-branes
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning AdS Propagators
• More on Supersymmetric and 2d Analogs of the SYK Model
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• High Energy Scattering in the AdS/CFT Correspondence
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