Entanglement equilibrium for higher order gravity

Bueno, Pablo; Min, Vincent S.; Speranza, Antony J.; Visser, Manus R.

doi:10.1103/physrevd.95.046003

Cited by 55 publications

(116 citation statements)

References 97 publications

(211 reference statements)

Supporting

Mentioning

112

Contrasting

Order By: Relevance

“…One could take the deformation (3.11) at face value and define the volume from the symplectic form δV higher = Ω higher (δ Y g, δg), but it is not clear to us if this is the right thing to do. The proposal of [71] for the generalized volume appears to be equivalent to doing the latter.…”

Section: Higher Derivativesmentioning

confidence: 99%

Complexity and the bulk volume, a new York time story

Belin

Lewkowycz

Sárosi

2019

J. High Energ. Phys.

119

172

View full text Add to dashboard Cite

We study the boundary description of the volume of maximal Cauchy slices using the recently derived equivalence between bulk and boundary symplectic forms. The volume of constant mean curvature slices is known to be canonically conjugate to "York time". We use this to construct the boundary deformation that is conjugate to the volume in a handful of examples, such as empty AdS, a backreacting scalar condensate, or the thermofield double at infinite time. We propose a possible natural boundary interpretation for this deformation and use it to motivate a concrete version of the complexity=volume conjecture, where the boundary complexity is defined as the energy of geodesics in the Kähler geometry of half sided sources. We check this conjecture for Bañados geometries and a mini-superspace version of the thermofield double state. Finally, we show that the precise dual of the quantum information metric for marginal scalars is given by a particularly simple symplectic flux, instead of the volume as previously conjectured.Here, we are denoting linearized deformations by |δΨ λ ≈ |Ψ λ+δλ − |Ψ λ , the bulk field φ is dual to the operator sourced by λ, its conjugate momentum is π, and Σ is a bulk initial value surface. This is the main result of [21] and it gives a

show abstract

Section: Higher Derivativesmentioning

confidence: 99%

Complexity and the bulk volume, a new York time story

Belin

Lewkowycz

Sárosi

2019

J. High Energ. Phys.

119

172

View full text Add to dashboard Cite

show abstract

“…This establishes in particular that K is constant on the constant s slices. 42 Instead of using (2.11) we could use α = ∇ · ζ/d = −C∂ s C −1 to writeα = u a ∇ a α = −C −1 ∂ s (C∂ s C −1 ). Inserting (B.5) then yieldsα| s=0 = −1/[L sinh(R * /L)], which again establishes the fact thatα| s=0 is independent of x.…”

Section: B Conformal Killing Time and Mean Curvaturementioning

confidence: 99%

“…And by replacing L → iL and setting R * = Lπ/2 we obtain for the Wheeler-DeWitt patch of AdS: C = L/ cosh s, where L is the AdS radius. 42 A degenerate case is the dS static patch (R * → ∞), since in that case K = 0 for all s, i.e. all the CMC slices have zero mean curvature, so there is no York time flow for the dS static patch.…”

Section: B Conformal Killing Time and Mean Curvaturementioning

confidence: 99%

Gravitational thermodynamics of causal diamonds in (A)dS

2019

View full text Add to dashboard Cite

A maximally symmetric causal diamond is a solution to Einstein's equation with a cosmological constant. We establish a Smarr formula for such diamonds and a "first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the "entanglement equilibrium" result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed. * jacobson@umd.edu † m.r.visser@uva.nl E Conformal transformation from Rindler space to causal diamond 55 F Acceleration of the conformal Killing flow 56 (3) Rindler horizon ⇣ ⇠ i < l a t e x i t s h a 1 _ b a s e 6 4 = " Z S b F s 6 J e H r C 0 A r l k C Y O j u o 0 P K O 0 = " > A A A B 6 n i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B i y U R Q Y 9 F L x 4 r 2 g 9 o Y 9 l s J + 3 S z S b s b o Q S + h O 8 e F D E q 7 / I m / / G b Z u D t j 4 Y e L w 3 w 8 y 8 I B F c G 9 f 9 d g o r q 2 v r G 8 X N 0 t b 2 z u 5 e e f + g q e N U M W y w W M S q H < l a t e x i t s h a 1 _ b a s e 6 4 = " A w 7 J B 7 u Q b N k z 9 S A 4 r 0 1 X c s L h w / I = " > A A A B 6 n i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B U 0 l E q M e i F 4 8 V 7 Q e 0 s W y 2 m 3 b p Z h N 2 J 0 I J / Q l e P C j i 1 V / k z X / j t s 1 B W x 8 M P N 6 b Y W Z e k E h h 0 H W / n c L a + s b m V n G 7 t L O 7 t 3 9 Q P j x q m T Q c z S i C t k k h r T 9 d w E / Y x q F E z y a a m X G p 5 Q N q Z D 3 r V U 0 Y g b P 5 u f O i V n V h m Q M N a 2 F J K 5 + n s i o 5 E x k y i w n R H F k V n 2 Z u J / X j f F 8 M r P h E p S 5 I o t F o W p J B i T 2 d 9 k I D R n K C e W U K a F v Z W w E d W U o U 2 n Z E P w l l 9 e J a 2 L q u d W v b v L S v 0 6 j 6 M I J 3 A K 5 + B B D e p w C w 1 o A o M h P M M r v D n S e X H e n Y 9 F a 8 H J Z 4 7 h D 5 z P H / G + j Y 8 = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " A w 7 J B 7 u Q b N k z 9 S A 4 r 0 1 X c s L h w / I = " > A A A B 6 n i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B U 0 l E q M e i F 4 8 V 7 Q e 0 s W y 2 m 3 b p Z h N 2 J 0 I J / Q l e P C j i 1 V / k z X / j t s 1 B W x 8 M P N 6 b Y W Z e k E h h 0 H W / n c L a + s b m V n G 7 t L O 7 t 3 9 Q P j x q m T Q c z S i C t k k h r T 9 d w E / Y x q F E z y a a m X G p 5 Q N q Z D 3 r V U 0 Y g b P 5 u f O i V n V h m Q M N a 2 F J K 5 + n s i o 5 E x k y i w n R H F k V n 2 Z u J / X j f F 8 M r P h E p S 5 I o t F o W p J B i T 2 d 9 k I D R n K C e W U K a F v Z W w E d W U o U 2 n Z E P w l l 9 e J a 2 L q u d W v b v L S v 0 6 j 6 ...

show abstract

“…The equivalence of δS| V = 0 and the Einstein equations can alternatively be derived from a 'first law of causal diamond mechanics' [8,9]. In a gravitational theory consisting of a metric and matter fields, to obtain such a first law one evaluates the relation (B.6) for the region Ξ = B with conformal Killing vector ξ satisfying ξ| ∂B = 0:…”

Section: Review Of Maximal Entanglement Principlementioning

confidence: 99%

The gravitational dynamics of kinematic space

Callebaut

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We show that the dynamics of the kinematic space of a 2-dimensional CFT is gravitational and described by Jackiw-Teitelboim theory. We discuss the first law of this 2-dimensional dilaton gravity theory to support the relation between modular Hamiltonian and dilaton that underlies the kinematic space construction. It is further argued that Jackiw-Teitelboim gravity can be derived from a 2-dimensional version of Jacobson's maximal vacuum entanglement hypothesis.

show abstract

Entanglement equilibrium for higher order gravity

Cited by 55 publications

References 97 publications

Complexity and the bulk volume, a new York time story

Complexity and the bulk volume, a new York time story

Gravitational thermodynamics of causal diamonds in (A)dS

The gravitational dynamics of kinematic space

Contact Info

Product

Resources

About