39 research outputs found
Charged R\'enyi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals
We calculate the R\'enyi entropy , for a spherical
entangling surface in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic
duals. R\'enyi entropies must obey some interesting inequalities by definition.
However, for Gauss-Bonnet couplings , larger than a specific value,
but still allowed by causality, we observe a violation of the inequality
, which is related to the existence of negative entropy black holes,
providing interesting restrictions in the bulk theory. Moreover, we find an
interesting distinction of the behaviour of the analytic continuation of
for imaginary chemical potential, between negative and
non-negative .Comment: 50 pages, 16 figures. v3: Version to appear in JHE
Entanglement Entropy and Duality in AdS(4)
Small variations of the entanglement entropy \delta S and the expectation
value of the modular Hamiltonian \delta E are computed holographically for
circular entangling curves in the boundary of AdS(4), using gravitational
perturbations with general boundary conditions in spherical coordinates.
Agreement with the first law of thermodynamics, \delta S = \delta E, requires
that the line element of the entangling curve remains constant. In this
context, we also find a manifestation of electric-magnetic duality for the
entanglement entropy and the corresponding modular Hamiltonian, following from
the holographic energy-momentum/Cotton tensor duality.Comment: 43 pages, 2 figures, v2: a few clarifications have been added; final
version to appear in Nucl. Phys.
An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory
We extend the entanglement entropy calculation performed in the seminal paper
by Srednicki for free real massive scalar field theories in 1+1, 2+1 and 3+1
dimensions. We show that the inverse of the scalar field mass can be used as an
expansion parameter for a perturbative calculation of the entanglement entropy.
We perform the calculation for the ground state of the system and for a
spherical entangling surface at third order in this expansion. The calculated
entanglement entropy contains a leading area law term, as well as subleading
terms that depend on the regularization scheme, as expected. Universal terms
are non-perturbative effects in this approach. Interestingly, this perturbative
expansion can be used to approximate the coefficient of the area law term, even
in the case of a massless scalar field in 2+1 and 3+1 dimensions. The presented
method provides the spectrum of the reduced density matrix as an intermediate
result, which is an important advantage in comparison to the replica trick
approach. Our perturbative expansion underlines the relation between the area
law and the locality of the underlying field theory.Comment: 35 pages, 5 figure
Static Elliptic Minimal Surfaces in AdS(4)
The Ryu-Takayanagi conjecture connects the entanglement entropy in the
boundary CFT to the area of open co-dimension two minimal surfaces in the bulk.
Especially in AdS(4), the latter are two-dimensional surfaces, and, thus,
solutions of a Euclidean non-linear sigma model on a symmetric target space
that can be reduced to an integrable system via Pohlmeyer reduction. In this
work, we invert Pohlmeyer reduction to construct static minimal surfaces in
AdS(4) that correspond to elliptic solutions of the reduced system, namely the
cosh-Gordon equation. The constructed minimal surfaces comprise a two-parameter
family of surfaces that include helicoids and catenoids in H(3) as special
limits. Minimal surfaces that correspond to identical boundary conditions are
discovered within the constructed family of surfaces and the relevant geometric
phase transitions are studied.Comment: 47 pages, 15 figure
Dressed Elliptic String Solutions on RxS^2
We obtain classical string solutions on RxS^2 by applying the dressing method
on string solutions with elliptic Pohlmeyer counterparts. This is realized
through the use of the simplest possible dressing factor, which possesses just
a pair of poles lying on the unit circle. The latter is equivalent to the
action of a single Backlund transformation on the corresponding sine-Gordon
solutions. The obtained dressed elliptic strings present an interesting
bifurcation of their qualitative characteristics at a specific value of a
modulus of the seed solutions. Finally, an interesting generic feature of the
dressed strings, which originates from the form of the simplest dressing factor
and not from the specific seed solution, is the fact that they can be
considered as drawn by an epicycle of constant radius whose center is running
on the seed solution. The radius of the epicycle is directly related to the
location of the poles of the dressing factor.Comment: 47 pages, 2 figure
Salient Features of Dressed Elliptic String Solutions on S
We analyse several physical aspects of the dressed elliptic strings
propagating on and of their counterparts in
the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are
divided into two wide classes; kinks which propagate on top of elliptic
backgrounds and those which are non-localised periodic disturbances of the
latter. The former class of solutions obey a specific equation of state that is
in principle experimentally verifiable in systems which realize the sine-Gordon
equation. Among both of these classes, there appears to be a particular class
of interest the closed dressed strings. They in turn form four distinct
subclasses of solutions. Unlike the closed elliptic strings, these four
subclasses, exhibit interactions among their spikes. These interactions
preserve a carefully defined turning number, which can be associated to the
topological charge of the sine-Gordon counterpart. One particular class of
those closed dressed strings realizes instabilities of the seed elliptic
solutions. The existence of such solutions depends on whether a superluminal
kink with a specific velocity can propagate on the corresponding elliptic
sine-Gordon solution. Finally, the dispersion relations of the dressed strings
are studied. A qualitative difference between the two wide classes of dressed
strings is discovered. This would be an interesting subject for investigation
in the dual field theory.Comment: 75 pages, 27 figure