91 research outputs found
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
Noncommutative Gauge Dynamics From The String Worldsheet
We show how string theory can be used to reproduce the one-loop two-point
photon amplitude in noncommutative U(1) gauge theory. Using a simple
realization of the gauge theory in bosonic string theory, we extract from a
string cylinder computation in the decoupling limit the exact one loop field
theory result. The result is obtained entirely from the region of moduli space
where massless open strings dominate. Our computation indicates that the
unusual IR/UV singularities of noncommutative field theory do not come from
closed string modes in any simple way.Comment: 19 pages, harvmac.tex, 2 figures, references added, typos correcte
Stringy effects in scrambling
In [1] we gave a precise holographic calculation of chaos at the scrambling
time scale. We studied the influence of a small perturbation, long in the past,
on a two-sided correlation function in the thermofield double state. A similar
analysis applies to squared commutators and other out-of-time-order one-sided
correlators [2-4]. The essential bulk physics is a high energy scattering
problem near the horizon of an AdS black hole. The above papers used Einstein
gravity to study this problem; in the present paper we consider stringy and
Planckian corrections. Elastic stringy corrections play an important role,
effectively weakening and smearing out the development of chaos. We discuss
their signature in the boundary field theory, commenting on the extension to
weak coupling. Inelastic effects, although important for the evolution of the
state, leave a parametrically small imprint on the correlators that we study.
We briefly discuss ways to diagnose these small corrections, and we propose
another correlator where inelastic effects are order one.Comment: 31 pages plus appendix, 9 figures v2: typos, references, added
comments, v3: reference
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