40 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
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
Dynamics of Supersymmetric Gauge Theory
We study the physics of the Seiberg-Witten and
Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of ,
and supersymmetric gauge theory. The
theory is confining and its effective Lagrangian is a
spontaneously broken abelian gauge theory. We identify some
features of its physics which see this internal structure, including a spectrum
of different string tensions. We discuss the limit ,
identify a scaling regime in which instanton and monopole effects survive, and
give exact results for the crossover from weak to strong coupling along a
scaling trajectory. We find a large hierarchy of mass scales in the scaling
regime, including very light bosons, and the absence of weak coupling. The
light 's leave a novel imprint on the effective dual magnetic theory. The
effective Lagrangian appears to be inadequate to understand the conventional
large limit of the confining theory.Comment: 28 pages, harvmac, 4 eps figures in separate uuencoded file. We have
extended this paper considerably, adding new results, discussion and figures.
In particular, we give exact formulas for masses and couplings along a
scaling trajectory appropriate to the large limit. These formulas display
a novel effect due to light electric bosons down to energy scales , deep in the weak coupling magnetic regim
Onset of Random Matrix Behavior in Scrambling Systems
The fine grained energy spectrum of quantum chaotic systems is widely
believed to be described by random matrix statistics. A basic scale in such a
system is the energy range over which this behavior persists. We define the
corresponding time scale by the time at which the linearly growing ramp region
in the spectral form factor begins. We call this time . The
purpose of this paper is to study this scale in many-body quantum systems that
display strong chaos, sometimes called scrambling systems. We focus on randomly
coupled qubit systems, both local and -local (all-to-all interactions) and
the Sachdev--Ye--Kitaev (SYK) model. Using numerical results for Hamiltonian
systems and analytic estimates for random quantum circuits we find the
following results. For geometrically local systems with a conservation law we
find is determined by the diffusion time across the system,
order for a 1D chain of qubits. This is analogous to the behavior
found for local one-body chaotic systems. For a -local system with
conservation law the time is order but with a different prefactor and
a different mechanism than the scrambling time. In the absence of any
conservation laws, as in a generic random quantum circuit, we find , independent of connectivity.Comment: 61+20 pages, minor errors corrected, and significant edits in Section