479 research outputs found
Fermionic Localization of the Schwarzian Theory
The SYK model is a quantum mechanical model that has been proposed to be
holographically dual to a -dimensional model of a quantum black hole. An
emergent "gravitational" mode of this model is governed by an unusual action
that that has been called the Schwarzian action. It governs a reparametrization
of a circle. We show that the path integral of the Schwarzian theory is
one-loop exact. The argument uses a method of fermionic localization, even
though the model itself is purely bosonic.Comment: 19+9 page
Two-dimensional conformal field theory and the butterfly effect
We study chaotic dynamics in two-dimensional conformal field theory through
out-of-time order thermal correlators of the form .
We reproduce bulk calculations similar to those of [1], by studying the large
Virasoro identity block. The contribution of this block to the above
correlation function begins to decrease exponentially after a delay of , where is the scrambling
time , and are the energy scales of the
operators.Comment: v1: 14 pages plus appendices, 2 figures. v2: references updated and
minor changes to the text. v3: minor error corrected in Appendix B, but the
conclusion is unchange
Black holes and the butterfly effect
We use holography to study sensitive dependence on initial conditions in
strongly coupled field theories. Specifically, we mildly perturb a thermofield
double state by adding a small number of quanta on one side. If these quanta
are released a scrambling time in the past, they destroy the local two-sided
correlations present in the unperturbed state. The corresponding bulk geometry
is a two-sided AdS black hole, and the key effect is the blueshift of the early
infalling quanta relative to the slice, creating a shock wave. We
comment on string- and Planck-scale corrections to this setup, and discuss
points that may be relevant to the firewall controversy.Comment: 29 pages, 4 figures. v2: references added/clarified, typos corrected.
v3: reference added, referencing clarifie
Multiple Shocks
Using gauge/gravity duality, we explore a class of states of two CFTs with a
large degree of entanglement, but with very weak local two-sided correlation.
These states are constructed by perturbing the thermofield double state with
thermal-scale operators that are local at different times. Acting on the dual
black hole geometry, these perturbations create an intersecting network of
shock waves, supporting a very long wormhole. Chaotic CFT dynamics and the
associated fast scrambling time play an essential role in determining the
qualitative features of the resulting geometries.Comment: 24 pages, 10 figures. v2: reference adde
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