Multitrace deformation of the Aharony-Bergman-Jafferis-Maldacena theory

Motivated by the study of big crunch singularities in asymptotically AdS4 space-times, we consider a marginal triple trace deformation of Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The deformation corresponds to adding a potential which is unbounded below. In a 't Hooft large N limit, the beta function for the triple trace deformation vanishes, which is consistent with the near-boundary behavior of the bulk fields. At the next order in the 1/N expansion, the triple trace couplings exhibit nontrivial running, which we analyze explicitly in the limit of zero 't Hooft coupling, in which the model reduces to an O(N)×O(N) vector model with large N. In this limit, we establish the existence of a perturbative UV fixed point, and we comment on possible nonperturbative effects. We also show that the bulk analysis leading to big crunch singularities extends to the Zk orbifold models dual to ABJM theory.