35 research outputs found
Perturbative entanglement entropy in nonlocal theories
Entanglement entropy in the vacuum state of local field theories exhibits an
area law. However, nonlocal theories at large N and strong coupling violate
this area law. In these theories, the leading divergence in the entanglement
entropy is extensive for regions smaller than the effective nonlocality scale
and proportional to this effective nonlocality scale for regions larger than
it. This raises the question: is a volume law a generic feature of nonlocal
theories, or is it only present at strong coupling and large N?
This paper investigates entanglement entropy of large regions in weakly
coupled nonlocal theories, to leading order in the coupling. The two theories
studied are phi^4 theory on the noncommutative plane and phi^4 theory with a
dipole type nonlocal modification using a fixed nonlocality scale. Both
theories are found to follow an area law to first order in the coupling, hence
no evidence is found for a volume law. This indicates that, perturbatively the
nonlocal interactions considered are not generating sufficient entanglement at
distances of the nonlocality scale to change the leading divergence, at least
to first order in the coupling. An argument against volume laws at higher
orders is also presented.Comment: 25 pages, 3 figures; v2 added reference
Holographic Entanglement and Poincare blocks in three dimensional flat space
We propose a covariant prescription to compute holographic entanglement
entropy and Poincare blocks (Global BMS blocks) in the context of
three-dimensional Einstein gravity in flat space. We first present a
prescription based on worldline methods in the probe limit, inspired by recent
analog calculations in AdS/CFT. Building on this construction, we propose a
full extrapolate dictionary and use it to compute holographic correlators and
blocks away from the probe limit.Comment: 46 pages, 6 figure
Higher Curvature Gravity from Entanglement in Conformal Field Theories
By generalizing different recent works to the context of higher curvature
gravity, we provide a unifying framework for three related results: (i) If an
asymptotically AdS spacetime computes the entanglement entropies of ball-shaped
regions in a CFT using a generalized Ryu-Takayanagi formula up to second order
in state deformations around the vacuum, then the spacetime satisfies the
correct gravitational equations of motion up to second order around AdS; (ii)
The holographic dual of entanglement entropy in higher curvature theories of
gravity is given by Wald entropy plus a particular correction term involving
extrinsic curvatures; (iii) CFT relative entropy is dual to gravitational
canonical energy (also in higher curvature theories of gravity). Especially for
the second point, our novel derivation of this previously known statement does
not involve the Euclidean replica trick.Comment: 12 pages, 2 figure
Inviolable energy conditions from entanglement inequalities
Via the AdS/CFT correspondence, fundamental constraints on the entanglement
structure of quantum systems translate to constraints on spacetime geometries
that must be satisfied in any consistent theory of quantum gravity. In this
paper, we investigate such constraints arising from strong subadditivity and
from the positivity and monotonicity of relative entropy in examples with
highly-symmetric spacetimes. Our results may be interpreted as a set of energy
conditions restricting the possible form of the stress-energy tensor in
consistent theories of Einstein gravity coupled to matter.Comment: 25 pages, 3 figures, v2: refs added, expanded discussion of strong
subadditivity constraints in sections 2.1 and 4.
From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
We consider states of holographic conformal field theories constructed by
adding sources for local operators in the Euclidean path integral, with the aim
of investigating the extent to which arbitrary bulk coherent states can be
represented by such Euclidean path-integrals in the CFT. We construct the
associated dual Lorentzian spacetimes perturbatively in the sources. Extending
earlier work, we provide explicit formulae for the Lorentzian fields to first
order in the sources for general scalar field and metric perturbations in
arbitrary dimensions. We check the results by holographically computing the
Lorentzian one-point functions for the sourced operators and comparing with a
direct CFT calculation. We present evidence that at the linearized level,
arbitrary bulk initial data profiles can be generated by an appropriate choice
of Euclidean sources. However, in order to produce initial data that is very
localized, the amplitude must be taken small at the same time otherwise the
required sources diverge, invalidating the perturbative approach.Comment: 36 pages, 3 figure