Space-time structures from IIB matrix model

We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite N to all orders of the perturbation theory. Space-time is shown to be inseparable, and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure a vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.