Instability of complex CFTs with operators in the principal series - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2021

Instability of complex CFTs with operators in the principal series

Dario Benedetti

Résumé

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.

Dates et versions

hal-03171415 , version 1 (16-03-2021)

Identifiants

Citer

Dario Benedetti. Instability of complex CFTs with operators in the principal series. Journal of High Energy Physics, 2021, 05, pp.004. ⟨10.1007/JHEP05(2021)004⟩. ⟨hal-03171415⟩
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