Non-Minimally Coupled Pseudoscalars in AdS_4 for Instantons in CFT_3

Abstract: For the 11-dimensional supergravity over AdS_4 x S^7/Z_k, beginning with a general 4-from ansatz and the main geometry unchanged, we get a tower of massive and tachyonic pseudoscalars. Indeed, the resultant equations can be assigned to the so-called $\phi^4$ actions of the non-minimally coupled scalar-tensor theories with a cosmological constant. We focus on a well-known tachyonic and a new massive bulk mode, which are singlet under the internal group and break all supersymmetries, associated with skew-whiffing and Wick-rotating of the background 4-from flux, respectively. The first one is the conformally coupled m^2=-2 pseudoscalar in the bulk of Euclidean AdS_4, where an exact instanton solution is found and a marginally triple-trace deformation with a proper dimension-1 operator produces an agreeing boundary solution with finite action. From the action evaluated on the solution, we estimate the decay rate of the vacuum tunneling mediated by the instanton. Another massive m^2=+4 mode, with the so-called non-minimal coupling parameter $\xi = - 1/3$, also breaks the conformal invariance and so, there is no exact solution. Then, based on the AdS_4/CFT_3 correspondence rules, we propose the dimension-4 ($\Delta_+ = +4$) boundary operator in the skew-whiffed (anti-M2-branes) theory to deform the boundary action- consisting of a singlet fermion, an original scalar and U(1) gauges fields- with and find some solutions to be matched with the bulk solutions.