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Stanford, Douglas

Publications and source records attributed to Stanford, Douglas.

16 records
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DOE OSTI2024

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.

1/N Expansion↗
DOE OSTI2024

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.

2D Gravity↗
DOE OSTI2023

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 𝔰 𝔩 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 𝔰 𝔩 2 , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 𝔰 𝔩 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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

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/disk2 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.

2D Gravity↗
DOE OSTI2022

Replica wormholes and the black hole interior

Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of entanglement entropy. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including JT gravity coupled to conformal matter and the SYK model. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.

2D gravity↗
DOE OSTI2022

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 sub-leading 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.

2D Gravity↗
DOE OSTI2020

Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory

The Hilbert space of a quantum system with internal global symmetry $\textit{G}$ decomposes into sectors labelled by irreducible representations of $\textit{G}$. If the system is chaotic, the energies in each sector should separately resemble ordinary random matrix theory. We show that such “sector-wise” random matrix ensembles arise as the boundary dual of two- dimensional gravity with a $\textit{G}$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of ’t Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with $\textit{G}$ symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal $\mathbb{Z}$ 2 symmetry.

2D Gravity↗
DOE OSTI2018

A spacetime derivation of the Lorentzian OPE inversion formula

Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Fermionic localization of the schwarzian theory

The SYK model is a quantum mechanical model that has been proposed to be holographically dual to a 1 + 1-dimensional model of a quantum black hole. An emergent “gravitational” mode of this model is governed by an unusual action that has been called the Schwarzian action. It governs a reparametrization of a circle. We show that the path integral of the Schwarzian theory is one-loop exact. Here, the argument uses a method of fermionic localization, even though the model itself is purely bosonic.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Diving into traversable wormholes: Diving into traversable wormholes

We study various aspects of wormholes that are made traversable by an interaction beween the two asymptotic boundaries. We concentrate on the case of nearly-math formula gravity and discuss a very simple mechanical picture for the gravitational dynamics. We derive a formula for the two sided correlators that includes the effect of gravitational backreaction, which limits the amount of information we can send through the wormhole. We emphasize that the process can be viewed as a teleportation protocol where the teleportee feels nothing special as he/she goes through the wormhole. We discuss some applications to the cloning paradox for old black holes. We point out that the same formula we derived for math formula gravity is also valid for the simple SYK quantum mechanical theory, around the thermofield double state. We present a heuristic picture for this phenomenon in terms of an operator growth model. Finally, we show that a similar effect is present in a completely classical chaotic system with a large number of degrees of freedom.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space

We study a two-dimensional dilaton gravity system, recently studied by Almheiri and Polchinski, which describes near-extremal black holes, or more generally, nearly AdS 2 spacetimes. The asymptotic symmetries of AdS 2 are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the AdS 2 geometry and they are explicitly broken by the small deformation away from AdS 2 . This pattern of spontaneous plus explicit symmetry breaking governs the gravitational backreaction of the system. It determines several gravitational properties such as the linear in temperature dependence of the near-extremal entropy as well as the gravitational corrections to correlation functions. These corrections include the ones determining the growth of out-of-time-order correlators that is indicative of chaos. These gravitational aspects can be described in terms of a Schwarzian derivative effective action for a reparametrization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Remarks on the Sachdev-Ye-Kitaev model

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2;R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev, which motivated us to work out the details of the ideas described there.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A bound on chaos

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

1/N Expansion↗