The power of Lorentzian wormholes

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 at 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 these Lorentzian wormhole spacetimes is gauge-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.

An integrable road to a perturbative plateau

“…In section 6.3 we explain the logical need for a Lorentzian interpretation of the cancellations and the universal scaling behavior (3.50) of late-time genus g wormholes, and preview how this comes about by thinking about Lorentzian topology change in JT gravity [38].…”

“…We will present this picture elsewhere in more detail, with concrete calculations in JT gravity [38]. It is quite elementary to proof this experimentally for fixed genus and generic spectral curve (2.15) by computing both sides for generic f k , but we leave explicit expressions out to spare the reader's eyes.…”

“…This explanation we think should be intrinsically Lorentzian. A proposal based on topology changing processes for how these powers of time can be explained, analogous to the double-cone [3], will be presented elsewhere [38].…”