Double-Trace Flows and the Swampland

TL;DR

This paper investigates non-supersymmetric conformal field theories obtained via double-trace deformations of superconformal theories, analyzing their spectra, correlation functions, and potential to evade swampland constraints.

Contribution

It provides a concrete example of a non-supersymmetric IR fixed point from double-trace deformations and computes key spectral data analytically in a large N setting.

Findings

Analytic computation of four-point functions under double-trace flow

Derivation of anomalous dimensions for double-trace operators

Discussion of the relation to swampland and weak gravity bounds

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 $\int\!{\cal O}^2$, where ${\cal O}$ 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.