Instability of complex CFTs with operators in the principal series
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.
Mots clés
Conformal Field Theory
1/N Expansion
field theory: conformal
tachyon: stability
group: conformal
analysis: harmonic
scaling: dimension
operator: primary
operator: scaling
model: tensor
operator product expansion
AdS/CFT correspondence
effective action
anti-de Sitter
perturbation
two-particle
Euclidean