An SYK wormhole under the microscope
Abstract
We derive a large-N wormhole saddle in the Sachdev-Ye-Kitaev (SYK) model for the variance of the thermal one-point function of a heavy operator across realizations of the microscopic couplings. We propose that this saddle describes a double trumpet geometry. In the double-scaling limit, we express the wormhole as a transition amplitude in an emergent bulk Hilbert space of chords connecting the two boundaries. In the Schwarzian limit, the chords proliferate and the wormhole defines a quantum transition amplitude in the open-universe Hilbert space of Jackiw-Teitelboim (JT) gravity. Comparing the SYK wormhole amplitude with its counterpart in JT gravity coupled to matter provides a direct test of the heavy-operator randomness hypothesis in SYK. The microscopic SYK couplings specify the α-parameters of the wormhole. For a fixed realization of the couplings, we compute the observable in the corresponding α-state. We provide the bulk wavefunction of the associated half-wormhole, which exhibits erratic correlations in the length basis that do not self-average. We extend the bulk description to the Hilbert space of a closed universe. We point out that the correlation chords from which the wormhole geometry emerges structurally resemble local observer worldlines.
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BibTeX
@misc{bettaque2026wormhole,
title = {{An SYK wormhole under the microscope}},
author = {Valérie Bettaque and Martin Sasieta and Brian Swingle and Alejandro Vilar López},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20699},
eprint = {2610.20699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20699},
}
RIS
TY - UNPB
TI - An SYK wormhole under the microscope
AU - Valérie Bettaque
AU - Martin Sasieta
AU - Brian Swingle
AU - Alejandro Vilar López
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20699
UR - https://arxiv.org/abs/2610.20699
AB - We derive a large-N wormhole saddle in the Sachdev-Ye-Kitaev (SYK) model for the variance of the thermal one-point function of a heavy operator across realizations of the microscopic couplings. We propose that this saddle describes a double trumpet geometry. In the double-scaling limit, we express the wormhole as a transition amplitude in an emergent bulk Hilbert space of chords connecting the two boundaries. In the Schwarzian limit, the chords proliferate and the wormhole defines a quantum transition amplitude in the open-universe Hilbert space of Jackiw-Teitelboim (JT) gravity. Comparing the SYK wormhole amplitude with its counterpart in JT gravity coupled to matter provides a direct test of the heavy-operator randomness hypothesis in SYK. The microscopic SYK couplings specify the α-parameters of the wormhole. For a fixed realization of the couplings, we compute the observable in the corresponding α-state. We provide the bulk wavefunction of the associated half-wormhole, which exhibits erratic correlations in the length basis that do not self-average. We extend the bulk description to the Hilbert space of a closed universe. We point out that the correlation chords from which the wormhole geometry emerges structurally resemble local observer worldlines.
ER -