Abstract
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 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.
Highlights
Wormholes are geometric shortcuts that connect distant points in spacetime
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
In the context of holography, an important puzzle is that geometries connecting two boundaries indicate that the partition function of the dual field theory does not factorize [7]
Summary
Wormholes are geometric shortcuts that connect distant points in spacetime. Their role in the Euclidean path integral has been hotly debated in the literature [1,2,3,4,5,6,7,8,9,10]. We refer to [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] for recent discussions on this issue This problem does not arise in Lorentzian signature because nontraversable wormholes have horizons, which make them consistent with the factorization of the field theory dual.
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