Higgs-like (pseudo)scalars in AdS₄, marginal and irrelevant deformations in CFT₃, and instantons onS³

Abstract：

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