Abstract
In gauge/gravity duality, the bulk double cone geometry has been argued to account for a key feature of the spectral form factor known as the ramp. This feature is deeply associated with quantum chaos in the dual field theory. The connection with the ramp has been demonstrated in detail for two-dimensional theories of bulk gravity, but it appears natural in higher dimensions as well. In a general bulk theory the double cone might thus be expected to dominate the semiclassical bulk path integral for the boundary spectral form factor in the ramp regime. While other known spacetime wormholes have been shown to be unstable to brane nucleation when they dominate over known disconnected (factorizing) solutions, we argue below that the double cone is stable to semiclassical brane nucleation at the probe-brane level in a variety of string- and M-theory settings. Possible implications for the AdS/CFT factorization problem are briefly discussed.
Highlights
ΔZ associated with differences between the partition function Z in any particular element of the ensemble and the ensemble-mean Z
While other known spacetime wormholes have been shown to be unstable to brane nucleation when they dominate over known disconnected solutions, we argue below that the double cone is stable to semiclassical brane nucleation at the probe-brane level in a variety of string- and M-theory settings
While the importance of this issue has been understood for some time, the issue has received renewed emphasis due to the recently-recognized role that replica wormholes play in allowing bulk gravitational path integrals to reproduce the Page curve associated with unitarity in black hole evaporation [21, 22] and the associated connections to true spacetime wormholes and ensembles of boundary theories [13, 22, 23]
Summary
We provide a conceptual orientation to the physics that will be studied in the rest of this work. We first review the double cone geometry in its role as an intrinsically-. Complex saddle for the bulk path integral computing the so-called spectral form factor. We describe what it will mean to study the stability of such complex saddles with respect to brane nucleation
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