Local modular Hamiltonians from the quantum null energy condition

Behind certain marginally trapped surfaces one can construct a geometry containing an extremal surface of equal, but not larger area. This construction underlies the Engelhardt-Wall proposal for explaining Bekenstein-Hawking entropy as a coarse-grained entropy. The construction can be proven to exist classically but fails if the Null Energy Condition is violated.Here we extend the coarse-graining construction to semiclassical gravity. Its validity is conjectural, but we are able to extract an interesting nongravitational limit. Our proposal implies Wall's ant conjecture on the minimum energy of a completion of a quantum field theory state on a halfspace. It further constrains the properties of the minimum energy state; for example, the minimum completion energy must be localized as a shock at the cut. We verify that the predicted properties hold in a recent explicit construction of Ceyhan and Faulkner, which proves our conjecture in the nongravitational limit. * bousso@lbl.gov †

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“…The definition of M differs from the 1+1 case only through an additional transverse integral over d d−2 y. It can be shown [30,31]…”

Section: Higher-dimensional Casementioning

confidence: 99%

From black hole entropy to energy-minimizing states in QFT

2020

Self Cite

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“…In QFT, it is fundamental for the study of relative entropy [17,18] and its many applications to energy and information inequalities [19][20][21]. In the context of the AdS/CFT correspondence, it is instrumental in the program of reconstructing a gravitational bulk from the holographic data [22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Entanglement Spectrum of Chiral Fermions on the Torus

Fries

Reyes

2019

Phys. Rev. Lett.

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We determine the reduced density matrix of chiral fermions on the torus, for an arbitrary set of disjoint intervals and generic torus modulus. We find the resolvent, which yields the modular Hamiltonian in each spin sector. Together with a local term, it involves an infinite series of bi-local couplings, even for a single interval. These accumulate near the endpoints, where they become increasingly redshifted. Remarkably, in the presence of a zero mode, this set of points "condenses" within the interval at low temperatures, yielding continuous non-locality. * Electronic address: pascal.fries@physik.uni-wuerzburg.de † Electronic address: iareyes@uc.cl

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“…In shock-wave collisions, QNEC is never saturated in the hydrodynamic regime, but it is saturated in the far-fromequilibrium region, regardless of whether NEC is valid. Reference [40] (see also [41]) conjectures that saturation of QNEC can lead to a simplified expression for (part of) the modular Hamiltonian of a half-space in vacuum. …”

Section: Discussionmentioning

confidence: 99%

Saturation of the quantum null energy condition in far-from-equilibrium systems

et al. 2018

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The quantum null energy condition (QNEC) is a new local energy condition that a general quantum field theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the entanglement entropy in the corresponding null direction. We present the first series of explicit computations of QNEC in a strongly coupled QFT, using holography. We consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For the vacuum and thermal phase, QNEC is always weaker than NEC. While for the homogeneous quench QNEC is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction.

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Local modular Hamiltonians from the quantum null energy condition

Cited by 36 publications

References 34 publications

From black hole entropy to energy-minimizing states in QFT

From black hole entropy to energy-minimizing states in QFT

Entanglement Spectrum of Chiral Fermions on the Torus

Saturation of the quantum null energy condition in far-from-equilibrium systems

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