The boundary dual of the bulk symplectic form

TL;DR

This paper explores the relationship between boundary wavefunction overlaps, Kahler structures, and bulk gravitational symplectic forms in holographic theories, revealing a deep geometric connection with potential applications in holography.

Contribution

It demonstrates that the Kahler form from boundary wavefunction overlaps matches the bulk gravitational symplectic form in holographic field theories.

Findings

Kahler structure arises from boundary overlaps in holography.

Boundary Kahler form equals bulk gravitational symplectic form.

Potential boundary method to compute volume variations of maximal slices.

Abstract

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.