A bstract Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is welldefined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a codimension2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the HubenyRangamaniTakayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime.more »
Baby Universes, Holography, and the Swampland
On the basis of a number of Swampland conditions, we argue that the Hilbert space of baby universe states must be onedimensional in a consistent theory of quantum gravity. This scenario may be interpreted as a type of “Gauss’s law for entropy” in quantum gravity, and provides a clean synthesis of the tension between Euclidean wormholes and a standard interpretation of the holographic dictionary, with no need for an ensemble. Our perspective relies crucially on the recentlyproposed potential for quantummechanical gauge redundancies between states of the universe with different topologies. We further comment on the possible exceptions in d ≤ 3 for this hypothesis and the role of an ensemble in holographic theories in the context of theories of quantum gravity in d = 2 (such as JT gravity and possible cousins in d = 3), which we argue are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity for which an ensemble plays no role.
 Award ID(s):
 1719924
 Publication Date:
 NSFPAR ID:
 10181586
 Journal Name:
 ArXivorg
 Page Range or eLocationID:
 1  25
 ISSN:
 23318422
 Sponsoring Org:
 National Science Foundation
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