Bulk Landau pole and unitarity of dual conformal field theory

Abstract

The singlet sector of the O(N) ϕ4-model in AdS4 at large-N, gives rise to a dual conformal field theory on the conformal boundary of AdS4, which is a deformation of the generalized free field. We identify and compute an AdS4 three-point one-loop fish diagram that controls the exact large-N dimensions and operator product coefficients (OPE) for all “double trace” operators as a function of the renormalized ϕ4-couplings. We find that the space of ϕ4-coupling is compact with a boundary at the bulk Landau pole. The dual CFT is unitary only in an interval of negative couplings bounded by the Landau pole where the lowest OPE coefficient diverges.