Local phase space and edge modes for diffeomorphism-invariant theories

Speranza, Antony J.

doi:10.1007/jhep02(2018)021

Cited by 121 publications

(243 citation statements)

References 81 publications

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“…In this sense, this situation in gravity may look slightly analogous to topological ordered systems, where gapless degrees of freedom appear on boundaries, and therefore the classical contribution to the gravitational entropy is often called "gravity edge modes". Refer to [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for recent discussions.…”

Section: Introductionmentioning

confidence: 99%

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Gravity edges modes and Hayward term

Takayanagi

Tamaoka

2020

J. High Energ. Phys.

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We argue that corner contributions in gravity action (Hayward term) capture the essence of gravity edge modes, which lead to gravitational area entropies, such as the black hole entropy and holographic entanglement entropy. We explain how the Hayward term and the corresponding edge modes in gravity are explained by holography from two different viewpoints. One is an extension of AdS/CFT to general spacetimes and the other is the AdS/BCFT formulation. In the final part, we explore how gravity edge modes and its entropy show up in string theory by considering open strings stuck to a Rindler horizon.

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Section: Introductionmentioning

confidence: 99%

“…Then, one obtains a well-defined classical system. In principle, one can quantize it for each boundary condition [12] (see also [13][14][15][16] as examples for gravitational subsystems). This choice corresponds to one of the superselection sectors in the light of the operator algebra of a subregion [41].…”

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confidence: 99%

Gravity edges modes and Hayward term

Takayanagi

Tamaoka

2020

J. High Energ. Phys.

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“…If one wanted to consider the situation without this gauge-fixing, one would have to introduce degrees of freedom which track the location of Σ. This would lead to a formalism reminiscent of the 'extended phase space' of[33][34][35]. However, an important difference is as follows.…”

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confidence: 99%

The holographic dual of the entanglement wedge symplectic form

Kirklin

2020

J high energy phys

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In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a maximisation of transition probabilities. Using a replica trick, we compute this holonomy for curves of reduced states in boundary subregions of holographic QFTs at large N , subject to changes of operator insertions on the boundary. It is shown that the Berry phase along Uhlmann parallel paths may be written as the integral of an abelian connection whose curvature is the symplectic form of the entanglement wedge. This generalises previous work on holographic Berry curvature.

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“…We always work with smooth vector fields as representatives of the symmetries (as opposed to the singular vector fields considered in [20]). Furthermore, as discussed above, the Poisson algebra of the charges in our case is isomorphic to the Lie algebra of symmetries with no additional central extension (in contrast with [4,7,20]). The central extension we obtain already exists in the structure of the spacetime symmetry algebra g CD .…”

Section: Central Charges and Area Of The Bifurcation Edgementioning

confidence: 94%

Symmetries, charges and conservation laws at causal diamonds in general relativity

Chandrasekaran

Prabhu

2019

J. High Energ. Phys.

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We study the covariant phase space of vacuum general relativity at the null boundary of causal diamonds. The past and future components of such a null boundary each have an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and boost supertranslations corresponding to angle-dependent rescalings of affine parameter along the null generators. Associated to these symmetries are charges and fluxes obtained from the covariant phase space formalism using the prescription of Wald and Zoupas. By analyzing the behavior of the spacetime metric near the corners of the causal diamond, we show that the fluxes are also Hamiltonian generators of the symmetries on the phase space. In particular, the supertranslation fluxes yield an infinite family of boost Hamiltonians acting on the gravitational data of causal diamonds. We show that the smoothness of the vector fields representing such symmetries at the bifurcation edge of the causal diamond implies suitable matching conditions between the symmetries on the past and future components of the null boundary. Similarly, the smoothness of the spacetime metric implies that the fluxes of all such symmetries is conserved between the past and future components of the null boundary. This establishes an infinite set of conservation laws for finite subregions in gravity analogous to those at null infinity. We also show that the symmetry algebra at the causal diamond has a non-trivial center corresponding to constant boosts. The central charges associated to these constant boosts are proportional to the area of the bifurcation edge, for any causal diamond, in analogy with the Wald entropy formula.

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Local phase space and edge modes for diffeomorphism-invariant theories

Cited by 121 publications

References 81 publications

Gravity edges modes and Hayward term

Gravity edges modes and Hayward term

The holographic dual of the entanglement wedge symplectic form

Symmetries, charges and conservation laws at causal diamonds in general relativity

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