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Douglas Stanford

Publications and source records attributed to Douglas Stanford.

At least 19 recordsLinked to original sources
arXiv2026

Negative shocks versus static patch holography

We study a version of de Sitter static patch holography in which the Euclidean gravitational path integral, with an observer worldline included, is conjectured to compute a trace. Motivated by recent evidence for this conjecture from the sphere path integral, we test it further by inserting operators along the observer worldline and computing two-point functions and out-of-time-ordered four-point correlators (OTOCs). We extend an earlier OTOC calculation by Kolchmeyer and Liu using the shockwave formalism, incorporating both observer recoil and gravitational backreaction. We find that the OTOC conflicts with two basic properties of a trace in a Hilbert space: cyclicity and positivity. The signaling feature of the shockwave geometry gives rise to two distinct resummations of the perturbative eikonal expansion, which are interchanged by cyclicity. Positivity is violated by the fact that the leading perturbative contribution causes the (regularized) OTOC to increase.

hep-th↗
arXiv2026

Growth and collapse of subsystem complexity under random unitary circuits

For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity is defined as the minimum number of local quantum channels to generate a given state from a product state to a good approximation. In $1+1$d, we prove that the complexity of subsystems of length $\ell$ smaller than half grows linearly in time $T$ at least up to $T = \ell / 4$ but becomes zero after time $T = \ell /2$ in the limit of a large local dimension, while the complexity of the complementary subsystem of length larger than half grows linearly in time up to exponentially late times. Using holographic correspondence, we give some evidence that the state complexity of the smaller subsystem should actually grow linearly up to time $T = \ell/2$ and then abruptly decay to zero.

quant-ph↗
arXiv2026

On the phase of the de Sitter density of states

The one-loop gravitational path integral around Euclidean de Sitter space $S^D$ has a complex phase that casts doubt on a state counting interpretation. Recently, it was proposed to cancel this phase by including an observer. We explore this proposal in the case where the observer is a charged black hole in equilibrium with the de Sitter horizon. We compute the phase of the one-loop determinant within a two-dimensional dilaton gravity reduction, using both numerical and analytical methods. Our results interpolate between previous studies of a probe geodesic observer and the Nariai solution. We also revisit the prescription for going from the Euclidean path integral to the state-counting partition function, finding a positive sign in the final density of states.

hep-th↗
arXiv2025

Cusps in 3d gravity

Three dimensional hyperbolic manifolds have accumulation points in the spectrum of their volumes, leading to a divergence in the sum over topologies. The limit points are cusped hyperbolic manifolds, and we propose to renormalize the sum by including the cusped manifold as a counterterm. This gives a reinterpretation of the zeta-function regularization procedure used by Maloney and Witten in the sum over SL(2,Z) black holes. For pure N = 1 supergravity, cusps with even spin structure can be used in a similar way. Cusps with odd spin structure are not needed to cancel any divergence, but they find an application by making the index nonzero.

hep-th↗
arXiv2024

Bulk thimbles dual to trace relations

The maximal giant graviton is a D-brane wrapping a maximal $S^3\subset S^5$ within $\text{AdS}_5\times S^5$. It represents an upper bound on the $R$ charge that can be carried by certain bulk states. We study the maximal giant and its half-BPS fluctuations, motivated by a recent proposal \cite{Lee:2023iil} connecting these fluctuations to trace relations in the boundary theory. In a computation of the partition function of half-BPS states, we find that the maximal giant is an unstable saddle point and that its Lefschetz thimble corresponds to the quantization of an imaginary phase space. The states resulting from the quantization of this phase space contribute negatively to the partition function and can be regarded as bulk duals of trace relations. Finally, we study a model for a path integral that would connect together components of the bulk half-BPS field space with different numbers of giants.

hep-th↗
arXiv2023

Scramblon loops

In large $N$ chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the ``scramblon.'' We study self-interactions of the scramblon in variants of the Sachdev-Ye-Kitaev model. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to out-of-time-order correlators becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature.

hep-th↗
arXiv2023

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the "chord Hilbert space." We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the $\mathfrak{sl}_2$ near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to $\mathfrak{sl}_2$, but with a non-standard action on the boundary time coordinate. One can make the action of $\mathfrak{sl}_2$ algebra more standard at the cost of extending the boundary circle to include some "fake" portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

hep-th↗
arXiv2023

A Mirzakhani recursion for non-orientable surfaces

We review Mirzakhani's recursion for the volumes of moduli spaces of orientable surfaces, using a perspective that generalizes to non-orientable surfaces. The non-orientable version leads to divergences when the recursion is iterated, from regions in moduli space with small crosscaps. However, the integral kernels of the recursion are well-defined and they map precisely onto the loop equations for a matrix integral with orthogonal symmetry class and classical density of eigenvalues proportional to $\sinh(2π\sqrt{E})$ for $E>0$. The recursion can be used to compute regularized volumes with a cutoff on the minimal size of a crosscap.

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arXiv2022

A convergent genus expansion for the plateau

We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of "encounters" in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.

hep-th↗
arXiv2022

Firewalls from wormholes

Spacetime wormholes can lead to surprises in black hole physics. We show that a very old black hole can tunnel to a white hole/firewall by emitting a large baby universe. We study the process for a perturbed thermofield double black hole in Jackiw-Teitelboim (JT) gravity, using the lowest order (genus one) spacetime wormhole that corresponds to single baby-universe emission. The probability for tunneling to a white hole is proportional to $t^2 e^{-2S}$ where $t$ is the age of the black hole and $S$ is the entropy of one black hole.

hep-th↗
arXiv2022

Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime

Black holes provide a window into the microscopic structure of spacetime in quantum gravity. Recently the quantum information contained in Hawking radiation has been calculated, verifying a key aspect of the consistency of black hole evaporation with quantum mechanical unitarity. This calculation relied crucially on recent progress in understanding the emergence of bulk spacetime from a boundary holographic description. Spacetime wormholes have played an important role in understanding the underpinnings of this result, and the precision study of such wormholes, in this and other contexts, has been enabled by the development of low-dimensional models of holography. In this white paper we review these developments and describe some of the deep open questions in this subject. These include the nature of the black hole interior, potential applications to quantum cosmology, the gravitational explanation of the fine structure of black holes, and the development of further connections to quantum information and laboratory quantum simulation.

hep-th↗
arXiv2022

Subleading Weingartens

Haar integrals over the unitary group contain subleading terms that are needed for unitarity. We study analogous effects in the time evolution operators of JT gravity and Brownian SYK. In JT gravity with bulk matter we find an explanation for the first subleading terms, and in Brownian SYK we find configurations that can explain the full series. An important role is played by slightly off-shell modes that are exponentially amplified by chaos.

hep-th↗
arXiv2022

Many-body chaos at weak coupling

The strength of chaos in large $N$ quantum systems can be quantified using $λ_L$, the rate of growth of certain out-of-time-order four point functions. We calculate $λ_L$ to leading order in a weakly coupled matrix $Φ^4$ theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.

hep-th↗
arXiv2021

Sphere and disk partition functions in Liouville and in matrix integrals

We compute the sphere and disk partition functions in semiclassical Liouville and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk^2 is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in JT gravity is infinite.

hep-th↗
arXiv2021

Many-Body Chaos in the Sachdev-Ye-Kitaev Model

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N = 60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $λ$, across a wide range in temperatures, including in the regime where $λ$ approaches the universal bound, $λ= 2π/β$.

hep-th↗
arXiv2021

Wormholes without averaging

After averaging over fermion couplings, SYK has a collective field description that sometimes has "wormhole" solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space -- "half-wormholes." The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.

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arXiv2021

On entanglement spreading in chaotic systems

We discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two constraints: one follows from the existence of an emergent light cone, and the other is a conjecture associated to the "entanglement velocity" $v_E$. We compare this model to new holographic and spin chain computations, and to an operator growth picture. Finally, we introduce a second way of computing the emergent light cone speed in holographic theories that provides a boundary dynamics explanation for a special case of entanglement wedge subregion duality in AdS/CFT.

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