Double-trace flows and the swampland

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>We explore the idea that large <jats:italic>N</jats:italic>, 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 <jats:italic>k</jats:italic>, deformed by <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$ {\displaystyle \int {\mathcal{O}}^2} $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:mo>∫</mml:mo> <mml:mrow> <mml:msup> <mml:mi>O</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mstyle> </mml:math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$ \mathcal{O} $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> 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<jats:italic>/N</jats:italic>. 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 <jats:italic>N</jats:italic> CFT<jats:sub>3</jats:sub> with an Einstein gravity dual.</jats:p>