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 = \( \frac{d}{2} \) + i r, with non-vanishing r ∈ 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.

我们证明了d维共形场理论（CFT）的不稳定性，在两个基本场的算子乘积展开中，尺度维为h = \（\ frac {d} {2} \） + i r的主算子具有非零[R ∈ℝ。从AdS / CFT的角度来看，这对应于众所周知的速动不稳定性，这与违反AdS _{d +1}中的Breitenlohner-Freedman约束有关；我们在这里直接为泛型d派生它多维CFT，可以通过将欧几里得共形基团的谐波分析应用于两粒子不可约（2PI）有效作用中的共形溶液的扰动来获得，作为多标量量子场理论的极限。讨论了一些明确的示例，例如，melonic张量模型和双标鱼网模型。