arXiv subjects

Jan de Boer

Publications and source records attributed to Jan de Boer.

At least 37 records · Page 2Linked to original sources

arXiv2022

Boundary and bulk notions of transport in the AdS$_3$/CFT$_2$ correspondence

We construct operators in holographic two-dimensional conformal field theory, which act locally in the code subspace as arbitrary bulk spacelike vector fields. Key to the construction is an interplay between parallel transport in the bulk spacetime and in kinematic space. We outline challenges, which arise when the same construction is extended to timelike vector fields. We also sketch several applications, including boundary formulations of the bulk Riemann tensor, dreibein, and spin connection, as well as an application to holographic complexity.

hep-th↗

arXiv2022

Cost of holographic path integrals

We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in $T\bar T$ deformed holographic CFTs. In Nielsen's geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be `optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which satisfy the physical properties of cost, and (3) the proposals are by construction UV-finite. The optimal path integral that prepares a given state is that with minimal cost, and cost proposals which reduce to the CV and CV2.0 complexity conjectures when the path integral is optimised are found, while bounded cost proposals based on gravitational action are not found. Related to our analysis of gravitational action-based proposals, we study bulk hypersurfaces with a constant intrinsic curvature of a specific value and give a Lorentzian version of the Gauss-Bonnet theorem valid in the presence of conical singularities.

hep-th↗

arXiv2022

Virasoro Entanglement Berry Phases

We study the parallel transport of modular Hamiltonians encoding entanglement properties of a state. In the case of 2d CFT, we consider a change of state through action with a suitable diffeomorphism on the circle: one that diagonalizes the adjoint action of the modular Hamiltonian. These vector fields exhibit kinks at the interval boundary, thus together with their central extension they differ from usual elements of the Virasoro algebra. The Berry curvature associated to state-changing parallel transport is the Kirillov-Kostant symplectic form on an associated coadjoint orbit, one which differs appreciably from known Virasoro orbits. We find that the boundary parallel transport process computes a bulk symplectic form for a Euclidean geometry obtained from the backreaction of a cosmic brane, with Dirichlet boundary conditions at the location of the brane. We propose that this gives a reasonable definition for the symplectic form on an entanglement wedge.

hep-th↗

arXiv2022

Frontiers of Quantum Gravity: shared challenges, converging directions

Understanding the quantum nature of spacetime and gravity remains one of the most ambitious goals of theoretical physics. It promises to provide key new insights into fundamental particle theory, astrophysics, cosmology and the foundations of physics. Despite this common goal, the community of quantum gravity researchers is sometimes seen as divided into sub-communities working on different, mutually exclusive approaches. In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and interaction between traditionally distinct approaches. In this White Paper we discuss some of the common themes which have seen a growing interest from various directions, and argue that focusing on them will help the quantum gravity community as a whole towards shared objectives.

hep-th↗

arXiv2022

OPE statistics from higher-point crossing

We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in $d>2$. For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries.

hep-th↗

arXiv2022

Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes

The Eigenstate Thermalization Hypothesis makes a prediction for the statistical distribution of matrix elements of simple operators in energy eigenstates of chaotic quantum systems. As a leading approximation, off-diagonal matrix elements are described by Gaussian random variables but higher-point correlation functions enforce non-Gaussian corrections which are further exponentially suppressed in the entropy. In this paper, we investigate non-Gaussian corrections to the statistical distribution of heavy-heavy-heavy OPE coefficients in chaotic two-dimensional conformal field theories. Using the Virasoro crossing kernels, we provide asymptotic formulas involving arbitrary numbers of OPE coefficients from modular invariance on genus-$g$ surfaces. We find that the non-Gaussianities are further exponentially suppressed in the entropy, much like the ETH. We discuss the implication of these results for products of CFT partition functions in gravity and Euclidean wormholes. Our results suggest that there are new connected wormhole geometries that dominate over the genus-two wormhole.

hep-th↗

arXiv2022

Generalized Spectral Form Factors and the Statistics of Heavy Operators

The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories. In this paper, we introduce generalized spectral form factors: new probes of quantum chaos sensitive to the dynamical data of a theory. These quantities can be studied using an effective theory of quantum chaos. We focus our attention on a particular combination of heavy-heavy-heavy OPE coefficients that generalizes the genus-2 partition function of two-dimensional CFTs, for which we define a spectral form factor. We probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random matrix component in the ergodic regime. The EFT of quantum chaos predicts that the genus-2 spectral form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.

hep-th↗

arXiv2021

Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity

We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present two versions, one with microscopic charge conservation and one with exponentially suppressed violations. They agree for correlation functions of simple operators, but differ in the variance of charged one-point functions at finite temperature. We then apply these ideas to holography and to gravitational low-energy effective theories with a global symmetry. We show that Euclidean wormholes predict a non-zero variance for charged one-point functions, which is incompatible with microscopic charge conservation. This implies that global symmetries in quantum gravity must either be gauged or explicitly broken by non-perturbative effects.

hep-th↗

arXiv2021

Complexity for Conformal Field Theories in General Dimensions

We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance functions can be understood in terms of the geometry of coadjoint orbits of the conformal group. We explicitly relate our circuits to timelike geodesics in anti-de Sitter space and the complexity metric to distances between these geodesics. We extend our method to circuits in other symmetry groups using a group theoretic generalization of the notion of coherent states.

hep-th↗

arXiv2021

Carroll symmetry, dark energy and inflation

Carroll symmetry arises from Poincaré symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state ${\cal E}+P=0$ for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with $w=-1$. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry. To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.

hep-th↗

arXiv2021

On Local and Integrated Stress-Tensor Commutators

We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

hep-th↗

arXiv2021

Random Statistics of OPE Coefficients and Euclidean Wormholes

We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS$_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.

hep-th↗

arXiv2021

Quantum hypothesis testing in many-body systems

One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.

quant-ph↗

arXiv2021

Spacetime as a quantum circuit

We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the "complexity equals volume" conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $T\bar T$, we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

hep-th↗

arXiv2020

Open Source Software for Efficient and Transparent Reviews

To help researchers conduct a systematic review or meta-analysis as efficiently and transparently as possible, we designed a tool (ASReview) to accelerate the step of screening titles and abstracts. For many tasks - including but not limited to systematic reviews and meta-analyses - the scientific literature needs to be checked systematically. Currently, scholars and practitioners screen thousands of studies by hand to determine which studies to include in their review or meta-analysis. This is error prone and inefficient because of extremely imbalanced data: only a fraction of the screened studies is relevant. The future of systematic reviewing will be an interaction with machine learning algorithms to deal with the enormous increase of available text. We therefore developed an open source machine learning-aided pipeline applying active learning: ASReview. We demonstrate by means of simulation studies that ASReview can yield far more efficient reviewing than manual reviewing, while providing high quality. Furthermore, we describe the options of the free and open source research software and present the results from user experience tests. We invite the community to contribute to open source projects such as our own that provide measurable and reproducible improvements over current practice.

cs.IR↗

arXiv2020

Topological waves in passive and active fluids on curved surfaces: a unified picture

We investigate the occurrence of topologically protected waves in classical fluids confined on curved surfaces. Using a combination of topological band theory and real space analysis, we demonstrate the existence of a system-independent mechanism behind topological protection in two-dimensional passive and active fluids. This allows us to formulate an index theorem linking the number of modes, determined by the topology of Fourier space, to the real space topology of the surface on which they are hosted. With this framework in hand, we review two examples of topological waves in two-dimensional fluids, namely oceanic shallow-water waves propagating on the Earth's rotating surface and momentum waves in active polar fluids spontaneously "flocking" on substrates endowed with a ${\rm U}(1)$ isometry (e.g. surfaces of revolution). Our work suggests some simple rules to engineer topological modes on surfaces in passive and active soft matter systems.

cond-mat.soft↗

arXiv2020

Non-Boost Invariant Fluid Dynamics

We consider uncharged fluids without any boost symmetry on an arbitrary curved background and classify all allowed transport coefficients up to first order in derivatives. We assume rotational symmetry and we use the entropy current formalism. The curved background geometry in the absence of boost symmetry is called absolute or Aristotelian spacetime. We present a closed-form expression for the energy-momentum tensor in Landau frame which splits into three parts: a dissipative (10), a hydrostatic non-dissipative (2) and a non-hydrostatic non-dissipative part (4), where in parenthesis we have indicated the number of allowed transport coefficients. The non-hydrostatic non-dissipative transport coefficients can be thought of as the generalization of coefficients that would vanish if we were to restrict to linearized perturbations and impose the Onsager relations. For the two hydrostatic and the four non-hydrostatic non-dissipative transport coefficients we present a Lagrangian description. Finally when we impose scale invariance, thus restricting to Lifshitz fluids, we find 7 dissipative, 1 hydrostatic and 2 non-hydrostatic non-dissipative transport coefficients.

hep-th↗

arXiv2019

Holographic Order from Modular Chaos

We argue for an exponential bound characterizing the chaotic properties of modular Hamiltonian flow of QFT subsystems. In holographic theories, maximal modular chaos is reflected in the local Poincare symmetry about a Ryu-Takayanagi surface. Generators of null deformations of the bulk extremal surface map to modular scrambling modes -positive CFT operators saturating the bound- and their algebra probes the bulk Riemann curvature, clarifying the modular Berry curvature proposal of arXiv:1903.04493.

hep-th↗