  Superconductivity at the interface between the insulators LaAlO3 and SrTiO3
has been tuned with the electric field effect. The data provide evidence for a
two dimensional quantum superconductor to insulator (2D-QSI) transition. Here
we explore the compatibility of this phase transition line with
Berezinskii-Kosterlitz-Thouless (BKT) behavior and a 2D-QSI transition. In an
intermediate regime, limited by a finite size effect, we uncover remarkable
consistency with BKT- criticality, weak localization in the insulating state
and non-Drude behavior in the normal state. Our estimates for the critical
exponents of the 2D-QSI-transition, z =1 and nu=3, suggest that it belongs to
the 3D-xy universality class.
