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Daniel Harlow

Publications and source records attributed to Daniel Harlow.

At least 19 recordsLinked to original sources
arXiv2026

Anti-scrambling and euclidean folds from observer correlators in de Sitter space

The de Sitter horizon behaves in a qualitatively different way from a black hole horizon, which poses a challenge to any attempt to develop a fundamental quantum description of de Sitter space. In this paper we gather some ``data'' on this problem using gravitational calculations, seeing that they lead to an ``anti-scrambling'' phenomenon that is contrary to the behavior of standard many-body quantum systems. We organize our discussion in terms of correlation functions computed on the worldline of an observer living in the spacetime, with the two-point function looking like a conventional thermal correlator but the four-point function showing anti-scrambling. We propose that anti-scrambling can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.

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arXiv2026

Observers, $\alpha$-parameters, and the Hartle-Hawking state

In this paper we extend recent ideas about observers and closed universes to theories where observers can be fluctuated into existence in the Hartle-Hawking state. This introduces a phenomenon that was not considered in these earlier discussions: the dominant transition from one cosmological state to another can go through a fluctuation that annihilates the universe and creates a new one. We nonetheless argue that the observer decoherence rule allows for the third-quantized description of such a theory to emerge from a factorizing holographic theory with a one-dimensional Hilbert space, without any need for $\alpha$-parameters. We also point out a close analogy between the observer rule in this context and the coarse-graining of the spectral form factor at late times for AdS black holes. Along the way we clarify several aspects of the relationship between holography, the gravitational path integral, and $\alpha$-parameters. We also explain why string theory scattering amplitudes do not lead to a one-dimensional Hilbert space on the worldsheet, despite being computed by a gravitational path integral with a sum over topology. Finally we point out that using the path integral to compute integrated local operators conditioned on an observer in the context of a theory with a landscape can lead to rather surprising conclusions. For example we argue that in a landscape with one AdS minimum and one dS minimum, both of which can support observers, an observer almost surely finds themself in dS and not AdS even if the boundary conditions are dual to a state with an observer in AdS.

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arXiv2025

Disjoint additivity and local quantum physics

Quantum systems of physical interest are often local, but there are at least three competing perspectives on how "locality" should be formalized: an algebraic framework, a path-integral framework, and a lattice framework. One puzzle in this competition is that systems with higher-form symmetries, which are perfectly local from the path-integral and lattice perspectives, can violate the algebraic principle of "additivity". In this paper, we propose a resolution to this puzzle by introducing a weaker locality principle, "disjoint additivity", which together with Haag duality should always be satisfied in local quantum systems. As evidence, we give examples in which disjoint additivity is preserved when ordinary additivity is violated; we show that Haag duality and disjoint additivity are satisfied in rather general lattice systems with local symmetry constraints; we give examples of nonlocal theories in which either disjoint additivity or Haag duality is violated; and finally we give examples of systems with nonlocal symmetry constraints in which disjoint additivity is violated, but can be restored by passing to a local "SymTFT" system in one higher dimension.

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arXiv2025

Observer complementarity for black holes and holography

We present a mathematical formulation of black hole complementarity based on recent rules for including the observer in quantum cosmology. We argue that this provides a self-consistent treatment of the interior of an evaporating black hole throughout its history, as well as the Antonini-Sasieta-Swingle-Rath configuration where a closed universe is entangled with a pair of AdS universes.

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arXiv2025

Quantum mechanics and observers for gravity in a closed universe

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer $Ob$ in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly $e^{S_{Ob}}$, where $S_{Ob}$ is the number of degrees of freedom of $Ob$. Moreover we argue that the errors in this description are exponentially small in $S_{Ob}$. We give evidence for this proposal using the gravitational path integral and the coding interpretation of holography, and we explain how similar effects arise in black hole physics in appropriate circumstances.

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arXiv2024

Phase space of Jackiw-Teitelboim gravity with positive cosmological constant

In this paper we construct the classical phase space of Jackiw-Teitelboim gravity with positive cosmological constant on spatial slices with circle topology. This turns out to be somewhat more intricate than in the case of negative cosmological constant; this phase space has many singular points and is not even Hausdorff. Nonetheless, it admits a group-theoretic description which is quite amenable to quantization.

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arXiv2023

Gauging spacetime inversions in quantum gravity

Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes $\mathcal{CRT}$ symmetry (in even dimensions usually combined with a rotation to become $\mathcal{CPT}$), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well. In this article we discuss what it means to gauge a spacetime inversion symmetry, and we explain some of the more unusual consequences of doing this. In particular we argue that the gauging of $\mathcal{CRT}$ is automatically implemented by the sum over topologies in the Euclidean gravity path integral, that in a closed universe the Hilbert space of quantum gravity must be a real vector space, and that in Lorentzian signature manifolds which are not time-orientable must be included as valid configurations of the theory. In particular we give an example of an asymptotically-AdS time-unorientable geometry which must be included to reproduce computable results in the dual CFT.

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arXiv2023

Black holes in quantum gravity

This chapter gives an overview of the quantum aspects of black holes, focusing on the black hole information problem, the counting of black hole entropy in string theory, and the emergence of spacetime in holography. It is aimed at a broad physics audience, and does not presuppose knowledge of string theory or holography.

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arXiv2022

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of "non-isometric codes protected by computational complexity". We show that many previous ideas, such as the existence of a large number of "null states", a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, "state-dependent/state-specific" operator reconstruction, and the "simple entropy" approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

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arXiv2022

Jerusalem Lectures on Black Holes and Quantum Information

In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to holography and the AdS/CFT correspondence, focusing on those aspects which are relevant for the black hole information problem.

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arXiv2022

Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity

In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, including the construction of traversable wormholes, the existence of a family of $SL(2,\mathbb{R})$ algebras acting on the matter fields, and the calculation of the scrambling time, can be recast as simple consequences of this algebra. We also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the "typical state" versions of the firewall paradox. Unlike the "Schwarzian" or "boundary particle" formalism, our techniques involve no unphysical degrees of freedom and naturally generalize to higher dimensions. We do a few higher-dimensional calculations to illustrate this, which indicate that the results we obtain in JT gravity are fairly robust.

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arXiv2022

The Weak Gravity Conjecture: A Review

The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. We review these related conjectures and the evidence for their validity in the string theory landscape. We also review a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments which claim the conjecture is plausible based on general principles, and quantitative arguments for various special cases or analogues of the conjecture. We also outline the implications of these conjectures for particle physics, cosmology, general relativity, and mathematics. Finally, we highlight important directions for future research.

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arXiv2021

A universal formula for the density of states in theories with finite-group symmetry

In this paper we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero density, this gives a new proof of the completeness hypothesis for finite gauge fields. Inspired by the generality of the argument we further propose that the formula applies at high energy in any quantum field theory with a finite-group global symmetry, and give some evidence for this conjecture.

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arXiv2021

Global symmetry, Euclidean gravity, and the black hole information problem

In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.

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arXiv2020

Covariant phase space with boundaries

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity "$B$", whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving $B$ emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

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arXiv2019

Simple holographic models of black hole evaporation

Several recent papers have shown a close relationship between entanglement wedge reconstruction and the unitarity of black hole evaporation in AdS/CFT. The analysis of these papers however has a rather puzzling feature: all calculations are done using bulk dynamics which are essentially those Hawking used to predict information loss, but applying ideas from entanglement wedge reconstruction seems to suggest a Page curve which is consistent with information conservation. Why should two different calculations in the same model give different answers for the Page curve? In this note we present a new pair of models which clarify this situation. Our first model gives a holographic illustration of unitary black hole evaporation, in which the analogue of the Hawking radiation purifies itself as expected, and this purification is reproduced by the entanglement wedge analysis. Moreover a smooth black hole interior persists until the last stages the evaporation process. Our second model gives an alternative holographic interpretation of the situation where the bulk evolution leads to information loss: unlike in the models proposed so far, this bulk information loss is correctly reproduced by the entanglement wedge analysis. This serves as an illustration that quantum extremal surfaces are in some sense kinematic: the time-dependence of the entropy they compute depends on the choice of bulk dynamics. In both models no bulk quantum corrections need to be considered: classical extremal surfaces are enough to do the job. We argue that our first model is the one which gives the right analogy for what actually happens to evaporating black holes, but we also emphasize that any complete resolution of the information problem will require an understanding of non-perturbative bulk dynamics.

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arXiv2019

The Factorization Problem in Jackiw-Teitelboim Gravity

In this note we study the $1+1$ dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle-Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in $2+1$ dimensions, which we'd then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.

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