Holographic matter: Deconfined string at criticality

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 field theory of closed loops which includes a compact two-form gauge field coupled with closed loops in one higher-dimensional space. Small fluctuations of the loop fields around a saddle point are identified as propagating strings. 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.