arXiv subjects

Donald Marolf

Publications and source records attributed to Donald Marolf.

At least 19 recordsLinked to original sources

arXiv2026

Superconformal indices and black hole saddles

The AdS/CFT correspondence implies that the superconformal index ${\mathcal I}$ in ${\mathcal N=4}$ SU(N) supersymmetric Yang-Mills theory can be computed using the dual bulk theory. In particular, in the limit of large $N$, the index should be given by a sum over appropriate saddles. However, ${\mathcal I}$ depends on potentials $\sigma, \tau, \vec \Delta$ and, at large ${\rm Im}\, \tau = {\rm Im}\, \sigma$, the CFT index ${\mathcal I}$ rapidly approaches $1$ at all values of $N$. As a result, black hole saddles associated with exponentially large contributions in $N$ cannot contribute in this limit. This in particular excludes saddles that were previously suggested to be relevant in such regimes. We thus consider an approach to the bulk path integral motivated by taking it to be defined as an integral over real Lorentz-signature spacetimes with codimension-2 singularities. This approach leads only to saddles that satisfy the above bound, and to the enforcement of this bound via Stokes phenomena. We also find similar results for bulk AdS$_4$ calculations of the ABJM superconformal index.

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arXiv2026

Dirichlet walls and the end of time

We study evolution in Einstein-Hilbert gravity with Dirichlet boundary conditions imposed on a finite surface. We argue that there are open sets of initial data where such evolutions terminate at finite times due to singularities that reach the boundary. In any dimension, the simplest such examples occur in cosmologies. However, in 2+1 dimensions we also show that Dirichlet walls initially outside a BTZ black hole can fall through the horizon, and that this also leads to generic singularities. A similar construction in higher dimensions leads to trapped surfaces that reach the wall, though the end result of such evolutions is more difficult to study.

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arXiv2026

How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral

We resolve a puzzle associated with the spherically-symmetric sector of the AdS$_4$ Einstein-Maxwell partition function with inverse temperature $\beta$. Since charge is quantized, the semiclassical limit of the partition function is expected to be given by a sum over complex black hole solutions obtained by shifting the associated chemical potential $\mu$ by $\frac{2\pi i n}{e \beta}$ in terms of the relevant charge quantum $e$. However, the sum over all such saddles turns out to diverge at any finite value of $\beta$. We therefore consider a definition of this partition function as an integral over a space of metrics that are real and of Lorentz-signature up to the presence of certain conical singularities. A Picard-Lefshetz analysis shows that only a finite subset of the above saddles contribute to our integral at finite $\beta$, and thus that the sum over such saddles converges. The low temperature limit is nonetheless associated with a convergent sum over all saddles that (as $\beta \rightarrow \infty$) approach the usual large real Euclidean black holes. We also analyze the analogous partition function for the (uncharged) BTZ black hole in the ensemble defined by fixing an angular velocity $\Omega$ up to shifts by $\frac{2\pi i m}{s \beta}$, where $s=\frac{1}{2}$ or $s=1$ depending on the presence of absence of fermionic states. In this case, at all $\beta$ we find that all saddles contribute and that the sum over saddles converges. We also comment briefly on the apparent lack of utility of the so-called KSW condition in our context.

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arXiv2026

Lorentzian Path Integrals and Jackiw-Teitelboim wormholes with imaginary scalars

The Lorentzian path integral was recently used to argue that standard Euclidean axion wormholes do not dominate computations of connected AdS/CFT partition functions. We now apply similar methods to study the seemingly-analogous Jackiw-Teitelboim wormholes constructed by Garcia-Garcia and Godet using Jackiw-Teitelboim gravity with an imaginary-valued minimally-coupled massless scalar field. However, this time we find that these wormholes do dominate our path integral for the relevant connected partition function. This supports the suggestion by Garcia-Garcia and Godet that contributions from such wormholes parallel the physics of the Sachdev-Ye-Kitaev model at complex couplings. The result also illustrates the sensitivity of wormhole contributions to details of the relevant physics.

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arXiv2026

Axion Wormholes and the AdS/CFT Factorization Problem

This work investigates the relevance of Euclidean and complex axion wormholes to the AdS/CFT factorization problem. We use a framework that defines bulk gravitational path integrals by integrating over a real Lorentz-signature contour and then, as needed, perhaps further analytically continuing the resulting functions of boundary conditions. For technical reasons we focus on the case of 2+1 bulk dimensions. The AdS boundary conditions (in any dimension) require us to impose Dirichlet boundary conditions on the standard Euclidean axion $\chi_E$. Fixing its asymptotic values on two boundary spheres to $\pm \chi_{E,\infty}$, we find such wormholes to be subdominant to a UV-sensitive endpoint contribution for $\chi_{E, \infty}$ near the real axis, and that (with our conventions) they become dominant only for $\chi_{E, \infty}$ near the negative imgainary axis. Furthermore, such wormholes are irrelevant to our computation for ${\rm Im} \chi_{E, \infty} >0$ (in the sense that the associated ascent contour fails to intersect the contour of integration). The relevance of the wormhole saddle for real positive $\chi_{E, \infty}$ is in fact a matter of choice, as the saddle then lies on a Stokes' line at which the relevant intersection number changes from zero to one.

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arXiv2026

The JLMS formula in a large code with approximate error correction

Gauge/gravity duality is often described as a quantum error correcting code. However, as seen in the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula, exact quantum error correction with complementary recovery (and thus entanglement wedge reconstruction) emerges only in the limit $G \to 0$. As a result, precise arguments controlling error terms have focused on what we call `small' codes which, as $G \to 0$, describe only perturbative excitations near a given classical solution. Such settings are quite restrictive and, in particular, they prohibit discussion of any modular flow that would change the classical background. As a result, they forbid consideration of modular flows generated by semiclassical bulk states at order-one modular parameters. In contrast, we present a single `large' code for the bulk theory that can accommodate such flows and, in particular, in the $G \to 0$ limit includes superpositions of states associated with distinct classical backgrounds. This large code is assembled from small codes that each satisfy an approximate Faulkner-Lewkowycz-Maldacena formula. In this extended setting we clarify the meaning of the (approximate) JLMS relation between bulk and boundary modular Hamiltonians and quantify its validity in an appropriate class of states.

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arXiv2025

Are $S^1\times S^2$ wormholes generic with large sources?

Euclidean path integrals can be used to prepare states of a Lorentzian QFT. So long as any sources are turned off on the $t=0$ surface, the resulting Lorentzian states all belong to the same Hilbert space. Constructing more states than allowed by the Lorentzian density of states means that the resulting states must be linearly dependent. For large amplitude sources and a fixed cutoff on energy, the AdS bulk dual of this effect has been conjectured to be captured by spacetime wormholes. Wormholes should then be generic in the presence of large such Euclidean sources. This hypothesis can be studied in a context with asymptotically locally AdS$_4$ boundaries of topology $S^1 \times S^2$ in which the wormhole is supported by a source for minimally-coupled massless bulk scalars. In preparation for a later more complete study, we consider here a preliminary toy version of the model in which the spacetimes are cohomogeneity-1, but with the consequence that the sources do not vanish at $t=0$. We then find that generic sources at large masses do {\it not} lead to wormholes. Along the way we map out the phase diagram for wormhole, thermal AdS, and black hole phases of our cohomogeneity-1 ansatz. We also numerically evaluate their stability by identifying negative modes. In parallel with the previously-studied case of $S^3$ boundaries, the results are analogous to those associated with the familiar Hawking-Page transition.

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arXiv2025

Holographic codes and bulk RG flows

We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the Faulkner-Lewkowycz-Maldacena formula and in its R\'enyi generalization. This provides a general quantum code perspective on the arguments of Susskind and Uglum. Specifically, given a 'UV' code with two-sided recovery and appropriately flat entanglement spectrum together with a set of 'seed' states in the UV code, we explicitly construct an 'IR' code with corresponding properties which contains the given seed states and is of minimal size in a sense we describe.

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arXiv2025

Euclidean wormholes stability analysis revisited

Previous studies of linearized stability of asymptotically flat Euclidean axion wormholes found that symmetric modes suffered from divergences. We show that such divergences were an artifact of a particular way of solving the constraints, and that a full treatment leads to finite actions for such modes. The modes must thus be included in a stability analysis. However, since the action for these modes turns out to be positive, this turns out not to affect previous statements about stability of axion wormholes. We also introduce a technique that allows us to show this positivity at a pseudo-analytic level that avoids heavy numerics. Our techniques should be useful to future studies of stabilities of other wormholes as well.

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arXiv2025

Constraints are not enough

The Euclidean Einstein-Hilbert action is well-known to be unbounded below and thus to raise many questions regarding the definition of the gravitational path integral. A variety of works since the late 1980's have suggested that this problem disappears when one fixes a foliation of the spacetime and imposes the corresponding gravitational constraints. However, we show here that this approach fails with various classes of boundary conditions imposed on the foliation: compact slices without boundary, asymptotically flat, or asymptotically locally anti-de Sitter slices. We also discuss the idea of fixing the scalar curvature and Wick-rotating the conformal factor, and show that it also fails to produce an action bounded from below.

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arXiv2025

Geometric Entropies and their Hamiltonian Flows

In holographic theories, the Hubeny-Rangamani-Takayanagi (HRT) area operator plays a key role in our understanding of the emergence of semiclassical Einstein-Hilbert gravity. When higher derivative corrections are included, the role of the area is instead played by a more general functional known as the geometric entropy. It is thus of interest to understand the flow generated by the geometric entropy on the classical phase space. In particular, the fact that the associated flow in Einstein-Hilbert or Jackiw-Teitelboim (JT) gravity induces a relative boost between the left and right entanglement wedges is deeply related to the fact that gravitational dressing promotes the von Neumann algebra of local fields in each wedge to type II. This relative boost is known as a boundary-condition-preserving (BCP) kink-transformation. In a general theory of gravity (with arbitrary higher-derivative terms), it is straightforward to show that the flow continues to take the above geometric form when acting on a spacetime where the HRT surface is the bifurcation surface of a Killing horizon. However, the form of the flow on other spacetimes is less clear. In this paper, we use the manifestly-covariant Peierls bracket to explore such flows in two-dimensional theories of JT gravity coupled to matter fields with higher derivative interactions. The results no longer take a purely geometric form and, instead, demonstrate new features that should be expected of such flows in general higher derivative theories. We also show how to obtain the above flows using Poisson brackets.

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arXiv2024

De Sitter quantum gravity and the emergence of local algebras

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy slices provides an interesting laboratory in which this emergence can be explored. In this context, the remaining isometries are gauge symmetries and, as a result, gauge-invariant observables cannot be localized. Instead, local physics can arise only through certain relational constructions. We explore such issues below for perturbative quantum gravity around de Sitter space. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal $S^d$ in dS$_{d+1}$, this approximation can be accurate only over regions in which the corresponding global time coordinate $t$ spans an interval $\Delta t \lesssim O(\ln G^{-1})$. In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dS$_{d+1}$ so long as those regions are located far to the future or past of such a minimal $S^d$. This in particular includes arbitrarily large parts of any static patch.

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arXiv2024

Euclidean and complex geometries from real-time computations of gravitational R\'enyi entropies

Gravitational R\'enyi computations have traditionally been described in the language of Euclidean path integrals. In the semiclassical limit, such calculations are governed by Euclidean (or, more generally, complex) saddle-point geometries. We emphasize here that, at least in simple contexts, the Euclidean approach suggests an alternative formulation in terms of the bulk quantum wavefunction. Since this alternate formulation can be directly applied to the real-time quantum theory, it is insensitive to subtleties involved in defining the Euclidean path integral. In particular, it can be consistent with many different choices of integration contour. Despite the fact that self-adjoint operators in the associated real-time quantum theory have real eigenvalues, we note that the bulk wavefunction encodes the Euclidean (or complex) R\'enyi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both R\'enyi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail.

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arXiv2024

Looking at extremal black holes from very far away

Near-extremal black holes are subject to large quantum effects, which modify their low-temperature thermodynamic behavior. Hitherto, these quantum effects were analyzed by separating the geometry into the near-horizon region and its exterior. It is desirable to understand and reproduce such corrections from the full higher-dimensional asymptotically flat or AdS geometry's perspective. We address this question in this article and fill this gap. Specifically, we find off-shell eigenmodes of the quadratic fluctuation operator of the Euclidean gravitational dynamics, with eigenvalues that vanish linearly with temperature. We illustrate this for BTZ and neutral black holes with hyperbolic horizons in AdS in Einstein-Hilbert theory, and for the charged black holes in Einstein-Maxwell theory. The linear scaling with Matsubara frequency, which is a distinctive feature of the modes, together with the fact that their wavefunctions localize close to the horizon as we approach extremality, identifies them as responsible for the aforementioned quantum effects. We provide a contour prescription to deal with the sign indefiniteness of the Euclidean Einstein-Maxwell action, which we derive to aid our analysis. We also resolve a technical puzzle regarding modes associated with rotational isometries in stationary black hole spacetimes.

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arXiv2024

On the nature of ensembles from gravitational path integrals

Spacetime wormholes in gravitational path integrals have long been interpreted in terms of ensembles of theories. Here we probe what sort of theories such ensembles might contain. Careful consideration of a simple $d=2$ topological model indicates that the Hilbert space structure of a general ensemble element fails to factorize over disconnected Cauchy-surface boundaries, and in particular that its Hilbert space ${\cal H}_{N_{CS\partial}}$ for $N_{CS\partial}$ Cauchy-surface boundaries fails to be positive definite when the number $N_{CS\partial}$ of disconnected such boundaries is large. This suggests a generalization of the AdS/CFT correspondence in which a bulk theory is dual to an ensemble of theories that deviate from standard CFTs by violating both locality and positivity (at least under certain circumstances). Since violations of positivity are undesirable, we propose that positivity-violating elements of the ensemble be removed when studying physics in asymptotically AdS spacetimes (or in other contexts in which Cauchy surfaces have asymptotic boundaries), perhaps reducing the ensemble to a single standard CFT. Nevertheless, properties of any remaining CFTs that are uncorrelated with positivity of ${\cal H}_{N_{CS\partial}}$ at large $N_{CS\partial}$will agree with those of typical elements of the full ensemble and may be computed using the ensemble average. On the other hand, elements that violate positivity at large $N_{CS\partial}$ can still have a positive-definite cosmological sector with $N_{CS\partial}=0$. Such elements then define a basis for a Hilbert space describing such cosmologies. In contrast to the cases in which Cauchy-surfaces are allowed to have boundaries, we argue that the resulting Hilbert space need not decohere into single-state theories. As a result, familiar physics might be more easily recovered from this new scenario.

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arXiv2024

Null states and time evolution in a toy model of black hole dynamics

Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states $e^S$ in a gravitational system much smaller than the number of states $e^{S_{\mathrm{p}}}$ predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves $N = O(e^S)$ of the possible $e^{S_{\mathrm{p}}}$ perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for $N\ll e^S$ (in which case no quantum extremal surfaces can arise). In particular, even for small $N$, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension $D \ll e^S$. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.

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arXiv2024

When left and right disagree: Entropy and von Neumann algebras in quantum gravity with general AlAdS boundary conditions

Euclidean path integrals for UV-completions of $d$-dimensional bulk quantum gravity were studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflection-positivity, and factorization. Sectors ${\cal H}_{\cal B}$ of the resulting Hilbert space were defined for any $(d-2)$-dimensional surface ${\cal B}$, where ${\cal B}$ may be thought of as the boundary $\partial\Sigma$ of a bulk Cauchy surface in a corresponding Lorentzian description, and where ${\cal B}$ includes the specification of boundary conditions for bulk fields. Cases where ${\cal B}$ was the disjoint union $B\sqcup B$ of two identical $(d-2)$-dimensional surfaces were studied in detail and, after the inclusion of finite-dimensional `hidden sectors,' were shown to provide a Hilbert space interpretation of the associated Ryu-Takayanagi entropy. The analysis was performed by constructing type-I von Neumann algebras $\mathcal A_L^B,\mathcal A_R^B$ that act respectively at the left and right copy of $B$ in $B\sqcup B$. Below, we consider the case of general ${\cal B} = B_L\sqcup B_R$ with $B_L,B_R$ distinct. For any $B_R$, we find that the von Neumann algebra at $B_L$ acting on ${\cal H}_{B_L\sqcup B_R}$ is a central projection of the corresponding type-I von Neumann algebra on the `diagonal' Hilbert space ${\cal H}_{B_L\sqcup B_L}$. As a result, the von Neumann algebras $\mathcal A_L^{B_L},\mathcal A_R^{B_L}$ defined in [1] using the diagonal Hilbert space coincide precisely with those defined using the full Hilbert space of the theory. A second implication is that, for any ${\cal H}_{B_L\sqcup B_R}$, including the same hidden sectors as in the diagonal case again provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. We also show the above central projections to satisfy consistency conditions that lead to a universal central algebra relevant to all choices of $B_L,B_R$.

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arXiv2024

Link-area commutators in AdS${}_3$ area-networks

Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most analogous to fixed-area states of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding HRT surface. However, such RTNs have flat entanglement spectra for all choices of $R, \bar R,$ while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS$_3$ Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.

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