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Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and spatial denoising is an integral part of the real-time graphics pipeline. The main insight presented in this paper is that we can optimize the samples used in stochastic sampling such that the post-processing error is minimized. The core of our method is an analytical loss function which measures post-filtering error for a class of integrands - multidimensional Heaviside functions. These integrands are an approximation of the discontinuous functions commonly found in rendering. Our analysis applies to arbitrary spatial and spatiotemporal filters, scalar and vector sample values, and uniform and non-uniform probability distributions. We show that the spectrum of Monte Carlo noise resulting from our sampling method is adapted to the shape of the filter, resulting in less noisy final images. We demonstrate improvements over state-of-the-art sampling methods in three representative rendering tasks: ambient occlusion, volumetric ray-marching, and color image dithering. Common use noise textures, and noise generation code is available at https://github.com/electronicarts/fastnoise., Comment: 18 pages, 12 figures

Gravitational subsystems with boundaries carry the action of an infinite-dimensional symmetry algebra, with potentially profound implications for the quantum theory of gravity. We initiate an investigation into the quantization of this corner symmetry algebra for the phase space of gravity localized to a region bounded by a 2-dimensional sphere. Starting with the observation that the algebra $\mathfrak{sdiff}(S^2)$ of area-preserving diffeomorphisms of the 2-sphere admits a deformation to the finite-dimensional algebra $\mathfrak{su}(N)$, we derive novel finite-$N$ deformations for two important subalgebras of the gravitational corner symmetry algebra. Specifically, we find that the area-preserving hydrodynamical algebra $\mathfrak{sdiff}(S^2)\oplus_{\mathcal{L}}\mathbb{R}^{S^2}$ arises as the large-$N$ limit of $\mathfrak{sl}(N,\mathbb C)\oplus\mathbb{R}$ and that the full area-preserving corner symmetry algebra $\mathfrak{sdiff}(S^2)\oplus_{\mathcal{L}}\mathfrak{sl}(2,\mathbb{R})^{S^2}$ is the large-$N$ limit of the pseudo-unitary group $\mathfrak{su}(N,N)$. We find matching conditions for the Casimir elements of the deformed and continuum algebras and show how these determine the value of the deformation parameter $N$ as well as the representation of the deformed algebra associated with a quantization of the local gravitational phase space. Additionally, we present a number of novel results related to the various algebras appearing, including a detailed analysis of the asymptotic expansion of the $\mathfrak{su}(N)$ structure constants, as well as an explicit computation of the full $\mathfrak{diff}(S^2)$ structure constants in the spherical harmonic basis. A consequence of our work is the definition of an area operator which is compatible with the deformation of the area-preserving corner symmetry at finite $N$., Comment: v3: 57 pages + Appendices + References = 99 pages; Typos fixed; Published in JHEP

The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner's famous classification of representations of the Poincar\'e group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincar\'e group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid., Comment: 44 pages + 10 pages bonus content, 1 figure

Progress in identifying the bulk microstate interpretation of the Ryu-Takayanagi formula requires understanding how to define entanglement entropy in the bulk closed string theory. Unfortunately, entanglement and Hilbert space factorization remains poorly understood in string theory. As a toy model for AdS/CFT, we study the entanglement entropy of closed strings in the topological A-model in the context of Gopakumar-Vafa duality. We will present our results in two separate papers. In this work, we consider the bulk closed string theory on the resolved conifold and give a self-consistent factorization of the closed string Hilbert space using extended TQFT methods. We incorporate our factorization map into a Frobenius algebra describing the fusion and splitting of Calabi-Yau manifolds, and find string edge modes transforming under a $q$-deformed surface symmetry group. We define a string theory analogue of the Hartle-Hawking state and give a canonical calculation of its entanglement entropy from the reduced density matrix. Our result matches with the geometrical replica trick calculation on the resolved conifold, as well as a dual Chern-Simons theory calculation which will appear in our next paper \cite{secondpaper}. We find a realization of the Susskind-Uglum proposal identifying the entanglement entropy of closed strings with the thermal entropy of open strings ending on entanglement branes. We also comment on the BPS microstate counting of the entanglement entropy. Finally we relate the nonlocal aspects of our factorization map to analogous phenomenon recently found in JT gravity., Comment: Typos corrected and citations added

Conference and social events provides an opportunity for people to interact and develop formal contacts with various groups of individuals. In this paper, we propose an efficient interaction mechanism in a pervasive computing environment that provide recommendation to users of suitable locations within a conference or expo hall to meet and interact with individuals of similar interests. The proposed solution is based on evaluation of context information to deduce each user's interests as well as bioinspired self-organisation mechanism to direct users towards appropriate locations.Simulation results have also been provided to validate our proposed solution.

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large $N$. We calculate entanglement entropy in the $1/N$ expansion by mapping the theory to a system of $N$ fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the "Boltzmann entropy", $\log \dim (R)$ per point of the entangling surface, which counts the number of distinct microstates, and the "Shannon entropy", $- \sum p_R \log p_R$, which captures fluctuations of the macroscopic state. We find that the entropy scales as $N^2$ in the large $N$ limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with $N$, and confirm this behaviour with numerical simulations. While the term of order $N$ is surprising from the point of view of the string dual - in which only even powers of $N$ appear in the partition function - we trace it to a breakdown of large $N$ counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory., Comment: 31 pages, 8 figures

Superrotations arise from singular vector fields on the celestial sphere in asymptotically flat space, and their finite integrated versions have been argued by Strominger and Zhiboedov to insert cosmic strings into the spacetime. In this work, we argue for an alternative definition of the action of superrotations on Minkowski space that avoids introducing any defects. This involves realizing the finite superrotation not as a diffeomorphism between spaces, but as a mapping of Minkowski space to itself that may be multivalued or non-surjective. This eliminates any defects in the bulk spacetime at the expense of allowing for defects in the boundary celestial sphere metric. We further explore the geometry of the spatial surfaces in the superrotated spaces, and note that they intersect null infinity at the singularity of the superrotation, causing a breakdown in the large $r$ asymptotic expansion there. To determine how these surfaces embed into Minkowski space, a derivation of the finite superrotation transformation is presented in both Bondi and Newman-Unti gauges. The latter is particularly interesting, since the superrotations are shown to preserve the hyperbolic slicing of Minkowski space in Newman-Unti gauge, and this gauge also provides a means for extending the geometry beyond the Bondi coordinate patch. We argue that the new interpretation for the action of superrotations on spacetime motivates consideration of a wider class of celestial sphere metrics and asymptotic symmetry groups., Comment: 24+8 pages, 8 figures

We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge expansion yields the expectation value of the bulk length operator plus the entropy of length fluctuations, in accordance with the Ryu--Takayanagi formula and its generalization due to Faulkner, Lewkowycz, and Maldacena. Special attention is paid to the conformal mode problem and its resolution by a choice of contour for the gravitational path integral., Comment: 25 pages, 1 figure. references updated in v2

A superweapon of modern physics superscribes a wide superset of phenomena, ranging from supernumerary rainbows to superfluidity and even possible supermultiplets., Comment: No essential information

Entanglement entropy is an important quantity in field theory, but its definition poses some challenges. The naive definition involves an extension of quantum field theory in which one assigns Hilbert spaces to spatial sub-regions. For two-dimensional topological quantum field theory we show that the appropriate extension is the open-closed topological quantum field theory of Moore and Segal. With the addition of one additional axiom characterizing the `entanglement brane' we show how entanglement calculations can be cast in this framework. We use this formalism to calculate modular Hamiltonians, entanglement entropy and negativity in two-dimensional Yang-Mills theory and relate these to singularities in the modular flow. As a byproduct we find that the negativity distinguishes between the `log dim R' edge term and the `Shannon' edge term. We comment on the possible application to understanding the Bekenstein-Hawking entropy in two-dimensional gravity., Comment: 34 pages, 1 figure, many diagrams, some taken from arXiv:math/0510664, references added

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory deformed by the irrelevant operator $T \overline{T}$. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough, Mezei and Verlinde. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the $T \overline{T}$ deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the $T \overline{T}$-deformed CFT is the holographic dual of a finite region of spacetime., Comment: 12 pages, 3 figures

The holographic principle posits that all quantum information in a region of spacetime is encoded on its boundary. While there is strong evidence for this principle in certain models of quantum gravity in asymptotically anti-de Sitter spacetime, it is yet to be established whether holography is a generic feature of quantum gravity, or a peculiar property of these models. The goal of the present work is to present a model of holographic reconstruction in the framework of perturbative quantum gravity in flat spacetime. Specifically, we consider a state in the single-particle sector of a quantum field theory and give a method to completely reconstruct the quantum state from measurement of the metric at spatial infinity. Our argument uses a relativistic generalization of the quantum-mechanical Wigner function, and gives an explicit mechanism by which the gravitational constraints encode quantum information holographically on the boundary. Moreover, it suggests how information about more general states might be recovered from soft charges at null infinity, with applications to the black hole information loss paradox., Comment: 4 pages + references

We explore the important fundamental question of how quantum information is localized in quantum gravity, in a perturbative approach. Familiar descriptions of localization of information, such as via tensor factorization of the Hilbert space or a net of commuting subalgebras of operators, conflict with basic gravitational properties -- specifically gauge invariance -- already at leading order in perturbation theory. However, previous work found that information can be classically localized in a region in a way such that measurements, including those of the gravitational field, outside the region are insensitive to that information, and only measure total Poincare charges. This paper shows that, working to leading order in the gravitational coupling, a similar quantum result holds, leading to a definition of a "gravitational splitting" on the Hilbert space for gravity. Such localization of information also argues against a role for "soft hair" in resolving the information problem for black holes. This basic mathematical structure plausibly plays a foundational role in the quantum description of gravity., Comment: 6 pages of text + refs. v2: minor corrections

A notion of localization of information within quantum subsystems plays a key role in describing the physics of quantum systems, and in particular is a prerequisite for discussing important concepts such as entanglement and information transfer. While subsystems can be readily defined for finite quantum systems and in local quantum field theory, a corresponding definition for gravitational systems is significantly complicated by the apparent nonlocality arising due to gauge invariance, enforced by the constraints. A related question is whether "soft hair" encodes otherwise localized information, and the question of such localization also remains an important puzzle for proposals that gravity emerges from another structure such as a boundary field theory as in AdS/CFT. This paper describes different approaches to defining local subsystem structure, and shows that at least classically, perturbative gravity has localized subsystems based on a split structure, generalizing the split property of quantum field theory. This, and related arguments for QED, give simple explanations that in these theories there is localized information that is independent of fields outside a region, in particular so that there is no role for "soft hair" in encoding such information. Additional subtleties appear in quantum gravity. We argue that localized information exists in perturbative quantum gravity in the presence of global symmetries, but that nonperturbative dynamics is likely tied to a modification of such structure., Comment: 12 pages + references

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies., Comment: 16 pages + appendices

We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the $\frac{\delta \text{Area}}{4G_N}$ term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this $\frac{\delta \text{Area}}{4G_N}$ term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space., Comment: 20 pages, 11 figures

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large $N$. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane., Comment: 37 pages, 12 figures. v3: Modified title and abstract

Quantum field theory - our basic framework for describing all non-gravitational physics - conflicts with general relativity: the latter precludes the standard definition of the former's essential principle of locality, in terms of commuting local observables. We examine this conflict more carefully, by investigating implications of gauge (diffeomorphism) invariance for observables in gravity. We prove a dressing theorem, showing that any operator with nonzero Poincare charges, and in particular any compactly-supported operator, in flat-spacetime quantum field theory must be gravitationally dressed once coupled to gravity, i.e. it must depend on the metric at arbitrarily long distances, and we put lower bounds on this nonlocal dependence. This departure from standard locality occurs in the most severe way possible: in perturbation theory about flat spacetime, at leading order in Newton's constant. The physical observables in a gravitational theory therefore do not organize themselves into local commuting subalgebras: the principle of locality must apparently be reformulated or abandoned, and in fact we lack a clear definition of the coarser and more basic notion of a quantum subsystem of the Universe. We discuss relational approaches to locality based on diffeomorphism-invariant nonlocal operators, and reinforce arguments that any such locality is state-dependent and approximate. We also find limitations to the utility of bilocal diffeomorphism-invariant operators that are considered in cosmological contexts. An appendix provides a concise review of the canonical covariant formalism for gravity, instrumental in the discussion of Poincare charges and their associated long-range fields., Comment: 19 pages, latex. v2: small wording changes/improvements; matches version to appear in Phys Rev D

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon., Comment: 46 pages. v2: Error corrected in appendix B, results unchanged

The gravitational Gauss law requires any addition of energy to be accompanied by the addition of gravitational flux. The possible configurations of this flux for a given source may be called gravitational hair, and several recent works discuss gravitational observables (`gravitational Wilson lines') which create this hair in highly-collimated `combed' configurations. We construct and analyze time-symmetric classical solutions of 2+1 Einstein-Hilbert gravity such as might be created by smeared versions of such operators. We focus on the AdS$_3$ case, where this hair is characterized by the profile of the boundary stress tensor; the desired solutions are those where the boundary stress tensor at initial time $t=0$ agrees precisely with its vacuum value outside an angular interval $[-\alpha,\alpha]$. At linear order in source strength the energy is independent of the combing parameter $\alpha$, but non-linearities cause the full energy to diverge as $\alpha \to 0$. In general, solutions with combed gravitational flux also suffer from what we call displacement from their naive location. For weak sources and large $\alpha$ one may set the displacement to zero by further increasing the energy, though for strong sources and small $\alpha$ we find no preferred notion of a zero-displacement solution. In the latter case we conclude that naively-expected gravitational Wilson lines do not exist. In the zero-displacement case, taking the AdS scale $\ell$ to infinity gives finite-energy flux-directed solutions that may be called asymptotically flat., Comment: 23+1 pages, 6 figures v2: Journal version; small editorial changes from v1

We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimension and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.

Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics. These can be thought of as operators that create a particle, together with its inseparable gravitational field, and reduce to usual field operators of quantum field theory in the weak-gravity limit; they include both Wilson-line operators, and those creating a Coulombic field configuration. We also describe operators creating the field of a particle in motion; as in the electromagnetic case, these are expected to help address infrared problems. An important characteristic of the quantum theory of gravity is the algebra of its observables. We show that the commutators of the simple observables of this paper are nonlocal, with nonlocality becoming significant in strong field regions, as predicted previously on general grounds., Comment: 31 pages, latex. v2: Misc. enhancements, detailed in comments in tex file; eliminated commutator not matching locality bound. v3: Corrected expression for the ADM momentum

We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a longstanding puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant., Comment: 41 pages, an extended version of arXiv:1412.1895

The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the entanglement entropy of edge modes: classical solutions determined by the electric field normal to the entangling surface. We explain how the heat kernel regularization applied to this term leads to the negative divergent expression found by Kabat. This calculation also resolves a recent puzzle concerning the logarithmic divergences of gauge fields in 3+1 dimensions., Comment: 6 + epsilon pages. v2: Simplified derivation, added references. Matches PRL version

We propose a quantum mechanical method of detecting weak vibrational disturbances inspired by the protocol of entanglement farming. We consider a setup where pairs of atoms in their ground state are successively sent through an optical cavity. It is known that in this way it is possible to drive that cavity toward a stable fixed-point state. Here we study how that fixed-point state depends on the time interval between pairs of atoms and on the distance between the cavity's mirrors. Taking advantage of an extremely precise resonance effect, we find that there are special values of these parameters where the fixed-point state is highly sensitive to perturbations, even harmonic vibrations with frequencies several orders of magnitude below the cavity's natural frequency. We propose that this sensitivity may be useful for high precision metrology., Comment: 10 pages, 5 figures. RevTeX 4.1

Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity., Comment: 12 pages. Invited article for Classical and Quantum Gravity special issue on Entanglement and Quantum Gravity

We propose a protocol by which entanglement can be extracted repeatedly from a quantum field. In analogy with prior work on entanglement harvesting, we call this protocol entanglement farming. It consists of successively sending pairs of unentangled particles through an optical cavity. Using non-perturbative Gaussian methods, we show that in certain generic circumstances this protocol drives the cavity field towards a non-thermal metastable state. This state of the cavity is such that successive pairs of unentangled particles sent through the cavity will reliably emerge significantly entangled. We calculate thermodynamic aspects of the harvesting process, such as energies and entropies, and also the long-term behavior beyond the few-mode approximation. Significant for possible experimental realizations is the fact that this entangling fixed point state of the cavity is reached largely independently of the initial state in which the cavity was prepared. Our results suggest that reliable entanglement farming on the basis of such a fixed point state should be possible also in various other experimental settings, namely with the to-be-entangled particles replaced by arbitrary qudits and with the cavity replaced by a suitable reservoir system., Comment: V2: Added Journal Reference. Title modified to match published version. 16 pages, 8 figures. RevTex 4.1

Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting results, leading to the question of whether the canonical approach is covariant, and whether the path integral approach is unitary. We show the unitarity of the covariant U(1) Maxwell theory, defined via the Wick rotation of a Euclidean path integral. We begin by gauge-fixing the path integral, taking care with zero modes, large gauge transformations, and nontrivial bundles. We find an extra geometric factor in the partition function that has been overlooked in previous work, coming from the zero mode of the gauge symmetry, which affects the entropy and stress-energy tensor. With this extra factor, the covariant calculation agrees with the canonical result for ultrastatic manifolds, and in D = 2. Finally, we argue that if there exists a unitary (but not necessarily covariant) canonical formulation, then the covariant formulation must also be unitary, even if the two approaches disagree., Comment: 10 pages

Quantum fluctuations of matter fields contribute to the thermal entropy of black holes. For free minimally-coupled scalar and spinor fields, this contribution is precisely the entanglement entropy. For gauge fields, Kabat found an extra negative divergent "contact term" with no known statistical interpretation. We compare this contact term to a similar term that arises for nonminimally-coupled scalar fields. Although both divergences may be interpreted as terms in the Wald entropy, we point out that the contact term for gauge fields comes from a gauge-dependent ambiguity in Wald's formula. Revisiting Kabat's derivation of the contact term, we show that it is sensitive to the treatment of infrared modes. To explore these infrared issues, we consider two-dimensional compact manifolds, such as Euclidean de Sitter space, and show that the contact term arises from an incorrect treatment of zero modes. In a manifestly gauge-invariant reduced phase space quantization, the gauge field contribution to the entropy is positive, finite, and equal to the entanglement entropy., Comment: 27 pages

We consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing the edge states in irreducible representations of the gauge group, the entropy of an arbitrary state is expressed as the sum of three positive terms: a term associated with the classical Shannon entropy of the distribution of boundary representations, a term that appears only for non-Abelian gauge theories and depends on the dimension of the boundary representations, and a term representing nonlocal correlations. The first two terms are the entropy of the edge states, and depend only on observables measurable at the boundary. These results are applied to several examples of lattice gauge theory states, including the ground state in the strong coupling expansion of Kogut and Susskind. In all these examples we find that the entropy of the edge states is the dominant contribution to the entanglement entropy., Comment: 8 pages. v2: added references, expanded derivation, matches PRD version

The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second class, except for a global, first-class part that generates time reparametrizations. A reduced phase space formulation is given in which the local part of the scalar constraint is solved formally for the lapse as a function of the 3 metric and its conjugate momentum. In the infrared limit the scalar constraint is linear in the square root of the lapse. For asymptotically flat boundary conditions the Hamiltonian is a sum of bulk constraints plus a boundary term that gives the total energy. This energy expression is identical to the one for Einstein-aether theory which, for static spherically symmetric solutions, is the usual Arnowitt-Deser-Misner energy of general relativity with a rescaled Newton constant., Comment: 8 pages, no figures. v2: added references, corrected minor typographical errors. v3: matches PRD version

The requirements for stability of a Lorentz violating theory are analyzed. In particular we conclude that Einstein-aether theory can be stable when its modes have any phase velocity, rather than only the speed of light as was argued in a recent paper., Comment: 4 pages. v2: matches PRD version

We consider a Lorentz-violating theory of inflation consisting of Einstein-aether theory with a scalar inflaton coupled bilinearly to the expansion of the aether. We determine the conditions for linearized stability, positive energy, and vanishing of preferred-frame post-Newtonian parameters, and find that all these conditions can be met. In homogeneous and isotropic cosmology, the inflaton-aether expansion coupling leads to a driving force on the inflaton that is proportional to the Hubble parameter. This force affects the slow-roll dynamics, but still allows for a natural end to inflation., Comment: 13 pages. v2: matches PRD version