Replica symmetry breaking in random matrix model: A toy model of wormhole networks

We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean AdS 2 background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.

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“…A similar scaling behavior of βcrit also appeared in the Gaussian matrix model before taking the doublescaling limit[56].…”

supporting

confidence: 66%

JT gravity, KdV equations and macroscopic loop operators

Okuyama

Sakai

2020

J. High Energ. Phys.

Self Cite

102

222

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“…since all 3 boundaries lie in the single connected component. The resulting combinatorics coincide with those emerging from random matrix ensembles [91].…”

Section: Jhep08(2020)044supporting

confidence: 54%

Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information

Marolf

Maxfield

2020

J. High Energ. Phys.

332

761

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In the 1980's, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to 'baby universes' and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore this structure in detail in simple topological models of the bulk that allow us to compute the full spectrum of associated boundary theories. The dimension of the asymptotically AdS Hilbert space turns out to become a random variable Z, whose value can be less than the naive number k of independent states in the theory. For k > Z, consistency arises from an exact degeneracy in the inner product defined by the gravitational path integral, so that many a priori independent states differ only by a null state. We argue that a similar property must hold in any consistent gravitational path integral. We also comment on other aspects of extrapolations to more complicated models, and on possible implications for the black hole information problem in the individual members of the above ensemble.

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“…However, if we naively take the large N limit at fixed temperature, the disconnected correlator always dominates over the connected correlators. Around the temperature T ∼ N −2/3 , the disconnected and connected contributions become comparable [19], but this temperature is pushed to zero as N → ∞ which implies that the disconnected part is always dominant at finite temperature. As discussed in [10,11], to focus on this temperature scale T ∼ N −2/3 one can take a certain double scaling limit, called the Airy limit of random matrix model, which we will consider in the next section.…”

Section: Jhep03(2021)073mentioning

confidence: 99%

Quenched free energy from spacetime D-branes

Okuyama

2021

J. High Energ. Phys.

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We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the generating function of correlators. It turns out that the resulting quenched free energy is a monotonically decreasing function of the temperature, as expected.

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Replica symmetry breaking in random matrix model: A toy model of wormhole networks

Cited by 19 publications

References 42 publications

JT gravity, KdV equations and macroscopic loop operators

JT gravity, KdV equations and macroscopic loop operators

Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information

Quenched free energy from spacetime D-branes

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