Instability of complex CFTs with operators in the principal series

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 + i r, with non-vanishing r is an element of 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.

Automated summary

This study demonstrates the instability in d-dimensional conformal field theories, related to a tachyonic instability in AdS/CFT theory and violation of the Breitenlohner-Freedman bound in AdS(d+1). By applying harmonic analysis for the Euclidean conformal group, the instability for d-dimensional CFTs derived directly for multiscalar quantum field theory limits.