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We investigate the gauge/gravity duality between the ${\cal N} = 6$mass-deformed ABJM theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the11-dimensional supergravity on LLM geometries withSO(2,1)$\times$SO(4)/${\mathbb Z}_k$ $\times$SO(4)/${\mathbb Z}_k$ isometry, interms of a KK holography, which involves quadratic order field redefinitions.As a non-trivial extension of the previous work arXiv:1612.05066, we implementthe KK mappings for various gauge invariant fields up to quadratic order toobtain 4-dimensional gravity fields. The non-linearity of the KK maps indicatesthat, in the current case, we can observe the true purpose of the non-linear KKholography of the LLM solutions. Using such KK holography procedure, we obtainthe vacuum expectation values of the chiral primary operator of conformaldimension $\Delta = 2$ in the large $N$ limit but with general $k$ and examinethe gauge/gravity duality for LLM solutions, which are represented bysquare-shaped Young diagrams. We also show that the vacuum expectation valuesof the massive KK graviton modes are vanishing as expected by thesupersymmetry.

Holography of Massive M2-brane Theory: Non-linear Extension