Double-Trace Flows and the Swampland

Abstract

We explore the idea that large $N$, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite $k$, deformed by $\int {\mathcal{O}}^2$, where $\mathcal{O}$ is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in $1/N$. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large $N$ CFT${}_3$ with an Einstein gravity dual.

25+13 pages. v2: refs added, minor clarifications

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• de Sitter Cosmology on an expanding bubble
• Putting the Boot into the Swampland
• Non-Supersymmetric AdS from String Theory
• AdS${}_8$ Solutions in Type II Supergravity
• Holographic Perspectives On Models Of Moduli Stabilization In M-Theory
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
• Emergent Supersymmetry at Large $N$
• A domain wall bound on anti-de Sitter vacua