Massive (pesudo) scalars in AdS4, SO(4) invariant solutions and holography

Abstract

We include a new 7-form ansatz in 11-dimensional supergravity over AdS4× S7/ Zk when the internal space is considered as a U(1) bundle on CP3. 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) × 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 AdS4 (or SO(3, 1) in its dS3 slicing). The corresponding bare operators are irrelevant in probe approximation; and to realize the AdS4/ CFT3 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 S3/ Zk 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.