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 {displaystyle 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 CFT3 with an Einstein gravity dual.
Highlights
There are recent conjectures in the affirmative, motivated in part by an absence of explicit constructions
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 O2, where O is the superconformal primary in the stress-tensor multiplet
Summary
Let us first quickly recall the definition of a double-trace flow. Consider a large N CFTd which contains a scalar conformal primary O of conformal dimension ∆ < d/2. In the holographic context [21,22,23,24,25,26,27,28], in which O is dual to a scalar field φ of mass squared m2 = ∆(∆ − d) in AdS units, there are two choices of normalizable boundary conditions when −d2/4 ≤ m2 ≤ −d2/4 + 1: Each of these corresponds to a unitary conformal dimension at one end of the RG flow triggered by (2.1). By choosing the ∆+ boundary condition on the dual bulk scalar field, the CFT will naively flow to a non-SUSY fixed point. This was briefly considered in [25, 38, 39].
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