Unambiguous phase spaces for subregions

Kirklin, Josh

doi:10.1007/jhep03(2019)116

Cited by 15 publications

(18 citation statements)

References 48 publications

(66 reference statements)

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“…This is the new, to our knowledge, use of gravitational edge modes of subregions to probe the curvature of their embedding spacetime. Edge modes have been subject to a lot of recent studies due to their relation to soft theorems and the memory effect [15], the construction of the physical phase space of subsystems in gauge theories [14,30,33,34], the definition of entanglement entropy [35,36], and, more speculatively, to the black hole information problem [16,40]. In our work, the relative edge mode frame of infinitesimally separated regions acquired a new physical interpretation as a gravitational connection with curvature that depends on the background spacetime.…”

Section: Modular Berry Holonomies In Holographymentioning

confidence: 86%

A modular sewing kit for entanglement wedges

Czech

Boer

et al. 2019

J. High Energ. Phys.

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We relate the Riemann curvature of a holographic spacetime to an entanglement property of the dual CFT state: the Berry curvature of its modular Hamiltonians. The modular Berry connection encodes the relative bases of nearby CFT subregions while its bulk dual, restricted to the code subspace, relates the edge-mode frames of the corresponding entanglement wedges. At leading order in 1/N and for sufficiently smooth HRRT surfaces, the modular Berry connection simply sews together the orthonormal coordinate systems covering neighborhoods of HRRT surfaces. This geometric perspective on entanglement is a promising new tool for connecting the dynamics of entanglement and gravitation.

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Section: Modular Berry Holonomies In Holographymentioning

confidence: 86%

A modular sewing kit for entanglement wedges

Czech

Boer

et al. 2019

J. High Energ. Phys.

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“…[67]). To achieve this, one needs to view the exterior region as a closed dynamical system in its own right, including a careful discussion of boundary conditions on the causal horizon (knowing these will be part identifying the correct C there), and it is likely that the "edge mode" or "center" degrees of freedom that arise when one defines a phase space for gravity in a subregion [17,[68][69][70][71][72] will play an important role. In this paper we have chosen not to study null boundaries, so we leave this for future work.…”

Section: Black Hole Entropymentioning

confidence: 99%

Covariant phase space with boundaries

Harlow

2020

J. High Energ. Phys.

171

340

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The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity “B”, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving B emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

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“…[10][11][12][13][14][15][16]. For gravitons much less is known, although there have been discussions about factorizability at the level of the classical phase space [17][18][19][20]. A computation of entanglement entropy for massless spin two fields across a sphere was also performed in [21].…”

Section: Introductionmentioning

confidence: 99%

Bulk entanglement entropy for photons and gravitons in AdS$_3$

2020

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We study quantum corrections to holographic entanglement entropy in AdS_33/CFT_22; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk U(1)U(1) gauge fields and gravitons, whose dynamics in AdS_33 are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton’s constant. We also consider excited states obtained by acting with the U(1)U(1) current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.

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Unambiguous phase spaces for subregions

Cited by 15 publications

References 48 publications

A modular sewing kit for entanglement wedges

A modular sewing kit for entanglement wedges

Covariant phase space with boundaries

Bulk entanglement entropy for photons and gravitons in AdS$_3$

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