Massive (pesudo)Scalars in AdS$_4$, SO(4) Invariant Solutions and Holography

Abstract

We include a new 7-form ansatz in 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is considered as a U(1) bundle on CP^3. After a general analysis of the ansatz, we take a special form of it and obtain a scalar equation from which we focus on a few massive bulk modes that are SU(4) x U(1) R-singlet and break all supersymmetries. The mass term breaks the scale invariance and so the (perturbative) solutions we obtain are SO(4) invariant in Euclidean AdS_4 (or SO(3,1) in its dS_3 slicing). The corresponding bare operators are irrelevant in probe approximation; and to realize the AdS_4/CFT_3 correspondence, we need to swap the fundamental representations of $SO(8)$ for supercharges with those for scalars and fermions. In fact, we have domain-walls arising from (anti)M5-branes wrapping around S^3/Z_k of the internal space with parity breaking scheme. As a result, the duals may be in three-dimensional U(N) or O(N) Chern-Simon models with matters in fundamental representations. Accordingly, we present dual boundary operators and build instanton solutions in a truncated version of the boundary ABJM action; and, because of the unboundedness of bulk potential from below, it is thought that they lead to big crunch singularities in the bulk.