  We examine the enhancement of the interfacial superconductivity between
LaAlO$_{3}$ and SrTiO$_{3}$ by an effective electric field. Through the
breaking of inversion symmetry at the interface, we show that a term coupling
the superfluid density and an electric field can augment the superconductivity
transition temperature. Microscopically, we show that an electric field can
also produce changes in the carrier density by relating the measured
capacitance to the density of states. Through the electron-phonon induced
interaction in bulk SrTiO$_{3}$, we estimate the transition temperature.
