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In this paper, we study the overlaps of wavefunctionals prepared by turningon sources in the Euclidean path integral. For nearby states, these overlapsgive rise to a Kahler structure on the space of sources, which is naturallyinduced by the Fubini-Study metric. The Kahler form obtained this way can alsobe thought of as a Berry curvature and, for holographic field theories, we showthat it is identical to the gravitational symplectic form in the bulk. Wediscuss some possible applications of this observation, in particular aboundary prescription to calculate the variation of the volume of a maximalslice.

The boundary dual of the bulk symplectic form