Subregion-subalgebra duality: Emergence of space and time in holography

Leutheusser, Sam; Liu, Hong

doi:10.1103/PhysRevD.111.066021

Subregion-subalgebra duality: Emergence of space and time in holography

Journal Article · Fri Mar 28 00:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.111.066021· OSTI ID:2543109

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In holographic duality, a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. We propose a formulation of duality for a general causally complete bulk spacetime region, called subregion-subalgebra duality, which provides a framework to describe how geometric notions in the gravity system, such as spacetime subregions, different notions of times, and causal structure, emerge from the dual CFT. Subregion-subalgebra duality generalizes and brings new insights into subregion-subregion duality (or equivalently entanglement wedge reconstruction). It provides a mathematically precise definition of subregion-subregion duality and gives an independent definition of entanglement wedges without using entropy. Geometric properties of entanglement wedges, including those that play a crucial role in interpreting the bulk as a quantum error correcting code, can be understood from the duality as the geometrization of the superadditivity of certain algebras. Using general boundary subalgebras rather than those associated with geometric subregions makes it possible to find duals for general bulk spacetime regions, including those not touching the boundary. Applying subregion-subalgebra duality to a boundary state describing a single-sided black hole also provides a precise way to define mirror operators.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0012567; SC0020360

OSTI ID:: 2543109

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 6 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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