The boundary dual of the bulk symplectic form

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 Kähler structure on the space of sources, which is naturally induced by the Fubini–Study metric. The Kähler 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.