Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
The boundary dual of the bulk symplectic form
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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.
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UNVERDICTED 3representative citing papers
A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a quantum generalization of the Hollands-Iyer-Wald identity.
A variational perturbative method using the inhomogeneous Jacobi equation computes first-order changes in holographic subregion complexity for strip and disk subsystems under boosted black brane perturbations in AdS4, with the linear term vanishing for spherical subsystems.
citing papers explorer
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Toward Krylov-based holography in double-scaled SYK
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
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Covariant phase space and the semi-classical Einstein equation
A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a quantum generalization of the Hollands-Iyer-Wald identity.
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Inhomogeneous Jacobi equation and Holographic subregion complexity
A variational perturbative method using the inhomogeneous Jacobi equation computes first-order changes in holographic subregion complexity for strip and disk subsystems under boosted black brane perturbations in AdS4, with the linear term vanishing for spherical subsystems.