93 research outputs found
Linear gravity from conformal symmetry
We perform a unified systematic analysis of dimensional, spin
representations of the isometry algebra of the maximally symmetric spacetimes
AdS, and dS. This allows us to explicitly
construct the effective low-energy bulk equations of motion obeyed by linear
fields, as the eigenvalue equation for the quadratic Casimir differential
operator. We show that the bulk description of a conformal family is given by
the Fierz-Pauli system of equations. For this is a massive gravity
theory, while for conserved currents we obtain Einstein gravity and
covariant gauge fixing conditions. This analysis provides a direct algebraic
derivation of the familiar AdS holographic dictionary at low energies, with
analogous results for Minkowski and de Sitter spacetimes.Comment: 21 pages, 1 figur
Eigenstate thermalization in the Sachdev-Ye-Kitaev model
The eigenstate thermalization hypothesis (ETH) explains how closed unitary
quantum systems can exhibit thermal behavior in pure states. In this work we
examine a recently proposed microscopic model of a black hole in AdS, the
so-called Sachdev-Ye-Kitaev (SYK) model. We show that this model satisfies the
eigenstate thermalization hypothesis by solving the system in exact
diagonalization. Using these results we also study the behavior, in
eigenstates, of various measures of thermalization and scrambling of
information. We establish that two-point functions in finite-energy eigenstates
approximate closely their thermal counterparts and that information is
scrambled in individual eigenstates. We study both the eigenstates of a single
random realization of the model, as well as the model obtained after averaging
of the random disordered couplings. We use our results to comment on the
implications for thermal states of the dual theory, i.e. the AdS black
hole.Comment: 36 pages, many figures; references added; matches published versio
Non-Abelian Berry Phases and BPS Monopoles
We study a simple quantum mechanical model of a spinning particle moving on a
sphere in the presence of a magnetic field. The system has two ground states.
As the magnetic field is varied, the ground states mix through a non-Abelian
Berry phase. We show that this Berry phase is the path ordered exponential of
the smooth SU(2) 't Hooft-Polyakov monopole. We further show that, by adjusting
a potential on the sphere, the monopole becomes BPS and obeys the Bogomolnyi
equations. For this choice of potential, it turns out that there is a hidden
supersymmetry underlying the system and the Bogomolnyi equations are analogous
to the tt* equations of Cecotti and Vafa. We conjecture that the Bogomolnyi
equations also govern the Berry phase of N=(2,2) supersymmetric sigma models
with other target spaces.Comment: 15 pages. v2: footnotes added to point the reader towards later
developments where conjectures made in this paper were subsequently proven. A
shortened version of this paper was published in PRL under the title "Scheme
for Building a 't Hooft-Polyakov Monopole
Phases of scrambling in eigenstates
We use the monodromy method to compute expectation values of an arbitrary
number of light operators in finitely excited ("heavy") eigenstates of
holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ
threshold, these behave thermally up to small corrections, with an effective
temperature determined by the heavy state. Below the threshold we find
oscillatory and not decaying behavior. As an application of these results we
compute the expectation of the out-of-time order arrangement of four light
operators in a heavy eigenstate, i.e. a six-point function. Above the threshold
we find maximally scrambling behavior with Lyapunov exponent . Below threshold we find that the eigenstate OTOC shows persistent
harmonic oscillations.Comment: 25 pages. 2 figures. v2 references added. v3 minor typos fixe
A gravity derivation of the Tisza-Landau Model in AdS/CFT
We derive the fully backreacted bulk solution dual to a boundary superfluid
with finite supercurrent density in AdS/CFT. The non-linear boundary
hydrodynamical description of this solution is shown to be governed by a
relativistic version of the Tisza-Landau two-fluid model to non-dissipative
order. As previously noted, the phase transition can be both first order and
second order, but in the strongly-backreacted regime at low charge q we find
that the transition remains second order for all allowed fractions of
superfluid density.Comment: 27 pages, 6 figures, 1 appendix; version published in PR
Hawking Radiation and Non-equilibrium Quantum Critical Current Noise
The dynamical scaling of quantum critical systems in thermal equilibrium may
be inherited in the driven steady-state, leading to universal
out-of-equilibrium behaviour. This attractive notion has been demonstrated in
just a few cases. We demonstrate how holography - a mapping between the quantum
critical system and a gravity dual - provides an illuminating perspective and
new results. Non-trivial out-of-equilibrium universality is particularly
apparent in current noise, which is dual to Hawking radiation in the
gravitational system. We calculate this in a 2-dimensional system driven by a
strong in-plane electric field and deduce a universal scaling function
interpolating between previously established equilibrium and
far-from-equilibrium current noise. Since this applies at all fields,
out-of-equilibrium experiments no longer require very high fields for
comparison with theory.Comment: revised version to appear in PRL, 5 page
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