  We investigate the gauge/gravity duality between the ${\cal N} = 6$
mass-deformed ABJ theory with U$_k(N+l)\times$U$_{-k}(N)$ gauge symmetry and
the 11-dimensional supergravity on LLM geometries with
SO(2,1)$\times$SO(4)/${\mathbb Z}_k\times$SO(4)/${\mathbb Z}_k$ isometry and
the discrete torsion $l$. For chiral primary operators with conformal
dimensions $\Delta=1,2$, we obtain the exact vacuum expectation values using
the holographic method in 11-dimensional supergravity and show that the results
depend on the shapes of droplet pictures in LLM geometries. The
$\frac{l}{\sqrt{N}}$ contributions from the discrete torsion $l$ for several
simple droplet pictures in the large $N$ limit are determined in holographic
vacuum expectation values. We also explore the effects of the orbifolding
${\mathbb Z}_k$ and the asymptotic discrete torsion $l$, on the gauge/gravity
duality dictionary and on the nature of the asymptotic limits of the LLM
geometries.
