A Truncation of 11-Dimensional Supergravity for Fubini-Like Instantons in AdS_4/CFT_3

Abstract

From a consistent Kaluza-Klein truncation of 11-dimensional supergravity over AdS_4 x CP^3 x S^1/Z_k, with a general 4-form ansatz, we arrive at a set of equations and solutions for the included fields. In particular, we have a bulk equation for a self-interacting (pseudo)scalar with arbitrary mass. By computing the energy-momentum tensors of the associated Einstein equations, to include the backreaction, and setting them to zero, we solve the resulting equations with the bulk one and get solutions corresponding to marginal and marginally relevant deformations of the boundary CFT_3, which break the conformal symmetry. These bulk (pseudo)scalars are SU(4) x U(1)-singlet and the corresponding solutions break all supersymmetries and parity because of the associated (anti)M-branes wrapping around specific and mixed internal and external directions. As a result and according to AdS_4/CFT_3 duality rules, we would realize the boundary counterpart in three-dimensional Chern-Simon U(N) field theories with matters in fundamental representations. In particular, we build a SO(4)-invariant Fubini-like instanton solution by setting a specific boundary Lagrangian. The resulting solution is used to describe the dynamics of thin-wall bubbles that cause instability and big crunch singularities in the bulk because of the unboundedness of the boundary double-hump potential from below. Relations to mass-deformed ABJM model, O(N) vector models and scale invariance breaking are also discussed. Meanwhile, we evaluate corrections for the background actions because of the bulk and boundary instantons.