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Euclidean wormhole in the SYK model
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We study a two-site Sachdev-Ye-Kitaev (SYK) model with complex couplings, and identify a low temperature transition to a gapped phase characterized by a constant in temperature free energy. This transition is observed without introducing a coupling between the two sites, and only appears after ensemble average over the complex couplings. We propose a gravity interpretation of these results by constructing an explicit solution of Jackiw-Teitelboim (JT) gravity with matter: a two-dimensional Euclidean wormhole whose geometry is the double trumpet. This solution is sustained by imaginary sources for a marginal operator, without the need of a coupling between the two boundaries. As the temperature is decreased, there is a transition from a disconnected phase with two black holes to the connected wormhole phase, in qualitative agreement with the SYK observation. The expectation value of the marginal operator is an order parameter for this transition. This illustrates in a concrete setup how a Euclidean wormhole can arise from an average over field theory couplings.
Forward citations
Cited by 4 Pith papers
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JT gravity on the worldline
Coupling a worldline observer to JT gravity replaces its evolution operator by an exactly computed average over fluctuating Euclidean times; the fluctuations are small in the disk but large on the double trumpet.
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Wormhole solutions with imaginary scalars set an Imaginary Distance Bound on analytic continuation of couplings, enforced by stringy effects that coincide with WGC and KSW in special cases.
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Time-like Janus Solution -- holographic global quantum quench --
A time-like Janus solution with imaginary deformation parameter is proposed as a holographic toy model of a global quantum quench, with partial consistency checks from CFT one-point functions and late-time entanglemen...
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Hot wormholes and chaos dynamics in a two-coupled SYK model
First numerical Lyapunov exponents for the unstable hot wormhole phase of the two-coupled SYK model, obtained via cooling and periodic-driving protocols.
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