Modular flow in JT gravity and entanglement wedge reconstruction

Journal Article · Mon Jun 24 00:00:00 EDT 2024 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep06(2024)151· OSTI ID:2576065

Gao, Ping ^[1]

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1. Rutgers Univ., Piscataway, NJ (United States)

It has been shown in recent works that JT gravity with matter with two boundaries has a type II_∞ algebra on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly nested in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III₁ subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the modular flow in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global RT surface in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III₁ algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II_∞ reduces to type III₁.

• Research Organization: Rutgers Univ., Piscataway, NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0010008
• OSTI ID: 2576065
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 6 Vol. 2024; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

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