  We study the gauge/gravity duality between bubbling geometries in type IIA
supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4
super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$
and the plane wave matrix model. We show that the geometries are realized as
field configurations in the strong coupling region of the gauge theories. On
the gravity side, the bubbling geometries can be mapped to electrostatic
systems with conducting disks. We derive integral equations which determine the
charge densities on the disks. On the gauge theory side, we obtain a matrix
integral by applying the localization to a 1/4-BPS sector of the gauge
theories. The eigenvalue densities of the matrix integral turn out to satisfy
the same integral equations as the charge densities on the gravity side. Thus
we find that these two objects are equivalent.
