  We derive a holographic dual for a gauged matrix model in general dimensions
from a first-principle construction. The dual theory is shown to be a closed
string field theory which includes a compact two-form gauge field coupled with
closed strings in one higher dimensional space. Possible phases of the matrix
model are discussed in the holographic description. Besides the confinement
phase and the IR free deconfinement phase, there can be two different classes
of critical states. The first class describes `holographic critical states'
where strings are deconfined in the bulk. The second class describes
`non-holographic critical states' where strings are confined due to
proliferation of topological defects for the two-form gauge field. This implies
that the critical states of the matrix model which admit holographic
descriptions with deconfined string in the bulk form novel universality classes
with non-trivial quantum orders which make the holographic critical states
qualitatively distinct from the non-holographic critical states. The signatures
of the non-trivial quantum orders in the holographic states are discussed.
Finally, we discuss a possibility that open strings emerge as fractionalized
excitations of closed strings along with an emergent one-form gauge field in
the bulk.
