  Transport measurements of the two-dimensional electron gas (2DEG) at the
LaAlO$_3$/SrTiO$_3$ interface have found a density of carriers much lower than
expected from the "polar catastrophe" arguments. From a detail
density-functional study, we suggest how this discrepancy may be reconciled. We
find that electrons occupy multiple subbands at the interface leading to a rich
array of transport properties. Some electrons are confined to a single
interfacial layer and susceptible to localization, while others with small
masses and extended over several layers are expected to contribute to
transport.
