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 O 2 , where 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 fourpoint 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.

Double-trace deformations of conformal correlations

“…Therefore, in these cases, δγ = γ IR (5.6) and we can use our formulas to read off the anomalous dimensions in the interacting IR CFT. The same observation was made in [46], where γ U V = 0 due to supersymmetry for UV-protected double-trace operators. We will denote γ IR simply by γ below.…”

“…Similarly, we can compute the change from UV to IR of the C ΦOO OPE coefficient by attaching two σ lines to the UV three-point function ΦOO . This was worked out explicitly in [46], following similar steps as described above. In terms of normalized squared OPE coefficients, the result is Note that for d = 3 and ∆ = 1, a IR OOO vanishes, which is a well-known result for the critical O(N ) model in d = 3 [51].…”

“…can be extracted introducing O(M ) projectors as explained in [46]. In fact, since the exchanged operator O(x) is an O(M ) singlet, the tensor in (4.45) is trivial, and role of the projectors simply cancels out when expanding in a given OPE channel.…”

The Swampland: Introduction and Review

“…A similar suggestion was also made in []. This conjecture was studied and tested further in []. In [] it was further argued that geometries which look locally like AdS also manifest such an instability.…”

AdS8 solutions in type II supergravity

“…See [19] for preliminary discussion. See also [20] for another recent proposal of non-supersymmetric holography.…”