arXiv subjects

Stefan Leichenauer

Publications and source records attributed to Stefan Leichenauer.

At least 37 records · Page 2Linked to original sources

arXiv2018

Energy is Entanglement

We compute the local second variation of the von Neumann entropy of a region in theories with a gravity dual. For null variations our formula says that the diagonal part of the Quantum Null Energy Condition is saturated in every state, thus providing an equivalence between energy and entropy. We prove that the formula holds at leading order in 1/N, and further argue that it will not be affected at higher orders. We conjecture that the QNEC is saturated in all interacting theories. We also discuss the special case of free theories, and the implications of our formula for the Averaged Null Energy Condition, Quantum Focusing Conjecture, and gravitational equations of motion. We show that the leading-order gravitational equations of motion, Einstein's equations, are equivalent to leading-order saturation of the QFC for Planck-width deformations.

hep-th↗

arXiv2017

The Quantum Null Energy Condition, Entanglement Wedge Nesting, and Quantum Focusing

We study the consequences of Entanglement Wedge Nesting for CFTs with holographic duals. The CFT is formulated on an arbitrary curved background, and we include the effects of curvature-squared couplings in the bulk. In this setup we find necessary and sufficient conditions for Entanglement Wedge Nesting to imply the Quantum Null Energy Condition in $d\leq 5$, extending its earlier holographic proofs. We also show that the Quantum Focusing Conjecture yields the Quantum Null Energy Condition as its nongravitational limit under these same conditions.

hep-th↗

arXiv2017

The Quantum Focusing Conjecture Has Not Been Violated

Recent work of Fu, Koeller, and Marolf shows that in $d\geq 5$ dimensions a nonzero Gauss-Bonnet coupling of either sign can lead to a pointwise violation of the Quantum Focusing Conjecture. This violation is due to the classical geometric terms appearing in the QFC. Since those geometric terms are properly understood as expectation values of operators in an effective field theory, we argue that they are only well-defined when smeared over a region at least as large as the cutoff scale of the theory (which may be the Planck scale). We find that this smearing prescription removes the pointwise violation found by Fu et al.. We comment on the relationship to similar issues encountered in the study of Entanglement Wedge Nesting in holography.

hep-th↗

arXiv2017

The Bayesian Second Law of Thermodynamics

We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically-evolving system degrades over time. The Bayesian Second Law can be written as $ΔH(ρ_m, ρ) + \langle \mathcal{Q}\rangle_{F|m}\geq 0$, where $ΔH(ρ_m, ρ)$ is the change in the cross entropy between the original phase-space probability distribution $ρ$ and the measurement-updated distribution $ρ_m$, and $\langle \mathcal{Q}\rangle_{F|m}$ is the expectation value of a generalized heat flow out of the system. We also derive refined versions of the Second Law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of the Jarzynski equality. We demonstrate the formalism using simple analytical and numerical examples.

cond-mat.stat-mech↗

arXiv2017

Local Modular Hamiltonians from the Quantum Null Energy Condition

The vacuum modular Hamiltonian $K$ of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltoninan for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads $K" = T_{vv}$. This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition --- an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor --- and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in $1/N$.

hep-th↗

arXiv2016

Geometric Constraints from Subregion Duality Beyond the Classical Regime

Subregion duality in AdS/CFT implies certain constraints on the geometry: entanglement wedges must contain causal wedges, and nested boundary regions must have nested entanglement wedges. We elucidate the logical connections between these statements and the Quantum Focussing Conjecture, Quantum Null Energy Condition, Boundary Causality Condition, and Averaged Null Energy Condition. Our analysis does not rely on the classical limit of bulk physics, but instead works to all orders in $G\hbar \sim 1/N$. This constitutes a nontrivial check on the consistency of subregion duality, entanglement wedge reconstruction, and holographic entanglement entropy beyond the classical regime.

hep-th↗

arXiv2016

Dynamics of the Area Law of Entanglement Entropy

We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.

hep-th↗

arXiv2016

Holographic Proof of the Quantum Null Energy Condition

We use holography to prove the Quantum Null Energy Condition (QNEC) at leading order in large-$N$ for CFTs and relevant deformations of CFTs in Minkowski space which have Einstein gravity duals. Given any codimension-2 surface $Σ$ which is locally stationary under a null deformation in the direction $k$ at the point $p$, the QNEC is a lower bound on the energy-momentum tensor at $p$ in terms of the second variation of the entropy to one side of $Σ$: $\langle T_{kk}\rangle \geq S"/2π\sqrt{h}$. In a CFT, conformal transformations of this inequality give results which apply when $Σ$ is not locally stationary. The QNEC was proven previously for free theories, and taken together with our result this provides strong evidence that the QNEC is a true statement about quantum field theory in general.

hep-th↗

arXiv2015

Proof of the Quantum Null Energy Condition

We prove the Quantum Null Energy Condition (QNEC), a lower bound on the stress tensor in terms of the second variation in a null direction of the entropy of a region. The QNEC arose previously as a consequence of the Quantum Focussing Conjecture, a proposal about quantum gravity. The QNEC itself does not involve gravity, so a proof within quantum field theory is possible. Our proof is somewhat nontrivial, suggesting that there may be alternative formulations of quantum field theory that make the QNEC more manifest. Our proof applies to free and superrenormalizable bosonic field theories, and to any points that lie on stationary null surfaces. An example is Minkowski space, where any point $p$ and null vector $k^a$ define a null plane $N$ (a Rindler horizon). Given any codimension-2 surface $Σ$ that contains $p$ and lies on $N$, one can consider the von Neumann entropy $S_\text{out}$ of the quantum state restricted to one side of $Σ$. A second variation $S_\text{out}^{\prime\prime}$ can be defined by deforming $Σ$ along $N$, in a small neighborhood of $p$ with area $\cal A$. The QNEC states that $\langle T_{kk}(p) \rangle \ge \frac{\hbar}{2π} \lim_{{\cal A}\to 0}S_\text{out}^{ \prime\prime}/{\cal A}$.

hep-th↗

arXiv2015

Entanglement Tsunami in (1+1)-Dimensions

We study the time dependence of the entanglement entropy of disjoint intervals following a global quantum quench in (1+1)-dimensional CFTs at large-$c$ with a sparse spectrum. The result agrees with a holographic calculation but differs from the free field theory answer. In particular, a simple model of free quasiparticle propagation is not adequate for CFTs with a holographic dual. We elaborate on the entanglement tsunami proposal of Liu and Suh and show how it can be used to reproduce the holographic answer.

hep-th↗

arXiv2015

A Quantum Focussing Conjecture

We propose a universal inequality that unifies the Bousso bound with the classical focussing theorem. Given a surface $σ$ that need not lie on a horizon, we define a finite generalized entropy $S_\text{gen}$ as the area of $σ$ in Planck units, plus the von Neumann entropy of its exterior. Given a null congruence $N$ orthogonal to $σ$, the rate of change of $S_\text{gen}$ per unit area defines a quantum expansion. We conjecture that the quantum expansion cannot increase along $N$. This extends the notion of universal focussing to cases where quantum matter may violate the null energy condition. Integrating the conjecture yields a precise version of the Strominger-Thompson Quantum Bousso Bound. Applied to locally parallel light-rays, the conjecture implies a Quantum Null Energy Condition: a lower bound on the stress tensor in terms of the second derivative of the von Neumann entropy. We sketch a proof of this novel relation in quantum field theory.

hep-th↗

arXiv2015

Thermal Corrections to Entanglement Entropy from Holography

We use holographic techniques to calculate the first thermal correction to the entanglement entropy of a cap-like region of a CFT defined on a sphere, successfully reproducing the field theory result. Since this is an order-one correction to the entropy in the large-$N$ expansion, quantum corrections to the holographic entanglement entropy formula are essential. The bulk calculation is made tractable using the same technical machinery recently used to derive the linearized Einstein equations in the bulk from the first law of entanglement entropy in the CFT.

hep-th↗

arXiv2014

Limits on New Physics from Black Holes

Black holes emit high energy particles which induce a finite density potential for any scalar field $ϕ$ coupling to the emitted quanta. Due to energetic considerations, $ϕ$ evolves locally to minimize the effective masses of the outgoing states. In theories where $ϕ$ resides at a metastable minimum, this effect can drive $ϕ$ over its potential barrier and classically catalyze the decay of the vacuum. Because this is not a tunneling process, the decay rate is not exponentially suppressed and a single black hole in our past light cone may be sufficient to activate the decay. Moreover, decaying black holes radiate at ever higher temperatures, so they eventually probe the full spectrum of particles coupling to $ϕ$. We present a detailed analysis of vacuum decay catalyzed by a single particle, as well as by a black hole. The former is possible provided large couplings or a weak potential barrier. In contrast, the latter occurs much more easily and places new stringent limits on theories with hierarchical spectra. Finally, we comment on how these constraints apply to the standard model and its extensions, e.g. metastable supersymmetry breaking.

hep-ph↗

arXiv2014

Disrupting Entanglement of Black Holes

We study entanglement in thermofield double states of strongly coupled CFTs by analyzing two-sided Reissner-Nordstrom solutions in AdS. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order $\log E/δE$ in units of the temperature. We conjecture that the parametric form of this timescale is universal.

hep-th↗

arXiv2013

Null Geodesics, Local CFT Operators and AdS/CFT for Subregions

We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical G_N=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the CFT. We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the AdS-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a continuous bulk reconstruction is only possible when every null geodesic in a given bulk subregion has an endpoint on the associated boundary subregion. This suggests that a subregion duality for AdS-Rindler, if it exists, must involve nonlocal CFT operators in an essential way.

hep-th↗

arXiv2013

A Consistent Effective Theory of Long-Wavelength Cosmological Perturbations

Effective field theory provides a perturbative framework to study the evolution of cosmological large-scale structure. We investigate the underpinnings of this approach, and suggest new ways to compute correlation functions of cosmological observables. We find that, in contrast with quantum field theory, the appropriate effective theory of classical cosmological perturbations involves interactions that are nonlocal in time. We describe an alternative to the usual approach of smoothing the perturbations, based on a path-integral formulation of the renormalization group equations. This technique allows for improved handling of short-distance modes that are perturbatively generated by long-distance interactions.

hep-th↗

arXiv2013

AdS black holes, the bulk-boundary dictionary, and smearing functions

In Lorentzian AdS/CFT there exists a mapping between local bulk operators and nonlocal CFT operators. In global AdS this mapping can be found through use of bulk equations of motion and allows the nonlocal CFT operator to be expressed as a local operator smeared over a range of positions and times. We argue that such a construction is not possible if there are bulk normal modes with exponentially small near boundary imprint. We show that the AdS-Schwarzschild background is such a case, with the horizon introducing modes with angular momentum much larger than frequency, causing them to be trapped by the centrifugal barrier. More generally, we argue that any barrier in the radial effective potential which prevents null geodesics from reaching the boundary will lead to modes with vanishingly small near boundary imprint, thereby obstructing the existence of a smearing function. While one may have thought the bulk-boundary dictionary for low curvature regions, such as the exterior of a black hole, should be as in empty AdS, our results demonstrate otherwise.

hep-th↗

arXiv2012

Light-sheets and AdS/CFT

One may ask whether the CFT restricted to a subset b of the AdS boundary has a well-defined dual restricted to a subset H(b) of the bulk geometry. The Poincare patch is an example, but more general choices of b can be considered. We propose a geometric construction of H. We argue that H should contain the set C of causal curves with both endpoints on b. Yet H should not reach so far from the boundary that the CFT has insufficient degrees of freedom to describe it. This can be guaranteed by constructing a superset of H from light-sheets off boundary slices and invoking the covariant entropy bound in the bulk. The simplest covariant choice is L, the intersection of L^+ and L^-, where L^+ (L^-) is the union of all future-directed (past-directed) light-sheets. We prove that C=L, so the holographic domain is completely determined by our assumptions: H=C=L. In situations where local bulk operators can be constructed on b, H is closely related to the set of bulk points where this construction remains unambiguous under modifications of the CFT Hamiltonian outside of b. Our construction leads to a covariant geometric RG flow. We comment on the description of black hole interiors and cosmological regions via AdS/CFT.

hep-th↗