  In this paper, we study the overlaps of wavefunctionals prepared by turning
on sources in the Euclidean path integral. For nearby states, these overlaps
give rise to a Kahler structure on the space of sources, which is naturally
induced by the Fubini-Study metric. The Kahler form obtained this way can also
be thought of as a Berry curvature and, for holographic field theories, we show
that it is identical to the gravitational symplectic form in the bulk. We
discuss some possible applications of this observation, in particular a
boundary prescription to calculate the variation of the volume of a maximal
slice.
