A Landau Pole in Conformal Field Theory
Résumé
The singlet sector of the $O(N),$$\phi^4$-model in AdS$_4$ at large-$N$, gives rise to a (non-local) dual conformal field theory on the conformal boundary of AdS$_4$, which is a deformation of the generalized free field. We identify and compute a AdS$_4$ 3-point 1-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 $\phi^4$-coupling. We find that the space of $\phi^4$-coupling is compact with a boundary at the bulk Landau pole where the lowest OPE coefficient diverges.