Instability of complex CFTs with operators in the principal series

Abstract

We prove the instability of $d$-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension $h=d/2+ir$, with non-vanishing $r\in \mathbb{R}$. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdS${}_{d+1}$; we derive it here directly for generic $d$-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

39 pages, 7 figures. v2: corrected a few typos; v3: added some references, matches published version

References in corpus (20)

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• More on Supersymmetric and 2d Analogs of the SYK Model
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
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• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Melonic Dominance in Subchromatic Sextic Tensor Models
• The tri-fundamental quartic model
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
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• The Inversion Formula and 6j Symbol for 3d Fermions

Cited by in corpus (6)

• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• The F-theorem in the melonic limit
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions