Reduction of 11D supergravity to AdS ₄ space, Instantons, Adomian solutions and CFT ₃ duals

Starting from 11-dimensional supergravity compactified on the space [Formula: see text] with a new 4-form flux, and solving the equations of motion and Bianchi identities, as a consistent Kaluza–Klein truncation, we arrive at nonlinear partial differential equations governing the dynamics of (pseudo)scalar fields in Euclidean [Formula: see text] space. By incorporating the backreaction on both the external and internal spaces, we derive equations of motion that correspond to exactly marginal and marginally irrelevant operators in the dual boundary field theory. Solving the scalar equations both exactly and in the probe approximation using the Adomian decomposition method, for the massless mode ([Formula: see text]), which exhibits properties of a Goldstone boson, and massive modes ([Formula: see text]), interpreted as Higgs-like excitations, we obtain exact and perturbative solutions suitable for near the boundary analyzes, respectively. These [Formula: see text]-invariant solutions represent instantons corresponding to tunneling between nearly degenerate vacua of a bulk Higgs-like potential, or bounces that describe true vacuum bubble nucleation from a false or metastable vacuum. To realize the desired [Formula: see text] singlet bulk (pseudo)scalars, which originate from (anti)M-branes wrapping internal space directions and break all supersymmetries and parity, we consider the exchange of the three fundamental representations of [Formula: see text] for the gravitino. Focusing on the [Formula: see text] sector of the boundary quiver gauge group in the three-dimensional Chern–Simons-matter theory, and retaining only one scalar and one fermion, we identify the dual marginal and irrelevant operators. By deforming the boundary action with these operators, we obtain closed-form solutions with finite Euclidean action, which are in fact small instantons localized on a three-sphere at infinity. Furthermore, we confirm the AdS 4 /CFT 3 state-operator correspondence at leading order.