Higgs-like (pseudo)Scalars in AdS$_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3

Abstract

With a 4-form ansatz of 11-dimensional supergravity over non-dynamical AdS$_4 \times S^7/Z_k$ background, with the internal space as a $S^1$ Hopf fibration on CP$^3$, we get a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS_4 space, may be viewed as arising from (anti)M-branes wrapping around internal directions in the (Wick-rotated) skew-whiffed M2-branes background (as the resulting theory is for anti-M2-branes) and so, realizing the modes after swapping the three fundamental representations $8_s, 8_c, 8_v$ of SO(8). Taking the backreaction on the external and internal spaces, we get massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT$_3$, and write a closed solution for the bulk equation and compute its correction to the background action. Next, considering the Higgs-like (breathing) mode $m^2=18$, having all supersymmetries, parity and scale-invariance broken, by solving the associated bulk equation with mathematical methods, especially the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in SU(4) x U(1)-singlet sectors of the ABJM model. Then, introducing new dual deformation $Δ_+$ = 3, 6 operators made of bi-fundamental scalars, fermions and U(1) gauge fields, we obtain SO(4)-invariant solutions as small instantons on a three-sphere with radius at infinity, which actually correspond to collapsing bulk bubbles leading to big-crunch singularities.