Abstract
As shown by Louko and Sorkin in 1995, topology change in Lorentzian signature involves spacetimes with singular points, which they called crotches. We modify their construction to obtain Lorentzian semiclassical wormholes in asymptotically AdS. These solutions are obtained by inserting crotches on known saddles, like the double-cone or multiple copies of the Lorentzian black hole. The crotches implement swap-identifications, and are classically located near an extremal surface. The resulting Lorentzian wormholes have an instanton action equal to their area, which is responsible for topological suppression in any number of dimensions.
We conjecture that including such Lorentzian wormhole spacetimes is equivalent to path integrating over all mostly Euclidean smooth spacetimes. We present evidence for this by reproducing semiclassical features of the genus expansion of the spectral form factor, and of a late-time two point function, by summing over the moduli space of Lorentzian wormholes. As a final piece of evidence, we discuss the Lorentzian version of West-Coast replica wormholes.
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Acknowledgments
We thank Luca Iliesiu, Don Marolf, Thomas Mertens, Mehrdad Mirbabayi, Pratik Rath, Ronak Soni, Douglas Stanford, Stephen Shenker, Mykhaylo Usatyuk and Ying Zhao for useful discussions. AB was supported by the ERC-COG Grant NP-QFT No. 864583 and by INFN Iniziativa Specifica GAST, and thanks Stanford’s SITP and Berkeley’s BCTP where part of this work was completed. JK is supported by NSF grant PHY-2207584 and PHY-1748958 and would like to thank KITP where part of this work was completed.
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Blommaert, A., Kruthoff, J. & Yao, S. The power of Lorentzian wormholes. J. High Energ. Phys. 2023, 5 (2023). https://doi.org/10.1007/JHEP10(2023)005
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DOI: https://doi.org/10.1007/JHEP10(2023)005