Geometric entropies and their Hamiltonian flows

Abstract In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional...

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Main Authors: Xi Dong, Donald Marolf, Pratik Rath
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP05(2025)085
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author Xi Dong
Donald Marolf
Pratik Rath
author_facet Xi Dong
Donald Marolf
Pratik Rath
author_sort Xi Dong
collection DOAJ
description Abstract In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.
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spelling doaj-art-1bebbe7925eb437684263dbc0b68bba52025-08-20T03:10:27ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025514210.1007/JHEP05(2025)085Geometric entropies and their Hamiltonian flowsXi Dong0Donald Marolf1Pratik Rath2Department of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaAbstract In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.https://doi.org/10.1007/JHEP05(2025)085Classical Theories of GravityAdS-CFT CorrespondenceGauge-Gravity Correspondence
spellingShingle Xi Dong
Donald Marolf
Pratik Rath
Geometric entropies and their Hamiltonian flows
Journal of High Energy Physics
Classical Theories of Gravity
AdS-CFT Correspondence
Gauge-Gravity Correspondence
title Geometric entropies and their Hamiltonian flows
title_full Geometric entropies and their Hamiltonian flows
title_fullStr Geometric entropies and their Hamiltonian flows
title_full_unstemmed Geometric entropies and their Hamiltonian flows
title_short Geometric entropies and their Hamiltonian flows
title_sort geometric entropies and their hamiltonian flows
topic Classical Theories of Gravity
AdS-CFT Correspondence
Gauge-Gravity Correspondence
url https://doi.org/10.1007/JHEP05(2025)085
work_keys_str_mv AT xidong geometricentropiesandtheirhamiltonianflows
AT donaldmarolf geometricentropiesandtheirhamiltonianflows
AT pratikrath geometricentropiesandtheirhamiltonianflows