21 research outputs found
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
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
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
Classical solutions of -deformed coset models
We obtain classical solutions of \l-deformed \s-models based on
and coset manifolds. Using two different
sets of coordinates, we derive two distinct classes of solutions. The first
class is expressed in terms of hyperbolic and trigonometric functions, whereas
the second one in terms of elliptic functions. We analyze their properties
along with the boundary conditions and discuss string systems that they
describe. It turns out that there is an apparent similarity between the
solutions of the second class and the motion of a pendulum.Comment: 36+9 pages, 8 figure
Entanglement of Harmonic Systems in Squeezed States
The entanglement entropy of a free scalar field in its ground state is
dominated by an area law term. It is noteworthy, however, that the study of
entanglement in scalar field theory has not advanced far beyond the ground
state. In this paper, we extend the study of entanglement of harmonic systems,
which include free scalar field theory as a continuum limit, to the case of the
most general Gaussian states, namely the squeezed states. We find the
eigenstates and the spectrum of the reduced density matrix and we calculate the
entanglement entropy. Finally, we apply our method to free scalar field theory
in 1+1 dimensions and show that, for very squeezed states, the entanglement
entropy is dominated by a volume term, unlike the ground-state case. Even
though the state of the system is time-dependent in a non-trivial manner, this
volume term is time-independent. We expect this behaviour to hold in higher
dimensions as well, as it emerges in a large-squeezing expansion of the
entanglement entropy for a general harmonic system.Comment: 44 pages + 29 pages appendix, 13 figure
Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
We study classical string solutions on RxS^2 that correspond to elliptic
solutions of the sine-Gordon equation. In this work, these solutions are
systematically derived inverting Pohlmeyer reduction and classified with
respect to their Pohlmeyer counterparts. These solutions include the spiky
strings and other well-known solutions, such as the BMN particle, the GKP
string or the giant magnons, which arise as special limits, and reveal many
interesting features of the AdS/CFT correspondence. A mapping of the physical
properties of the string solutions to those of their Pohlmeyer counterparts is
established. An interesting element of this mapping is the correspondence of
the number of spikes of the string to the topological charge in the sine-Gordon
theory. In the context of the sine-Gordon/Thirring duality, the latter is
mapped to the Thirring model fermion number, leading to a natural
classification of the solutions to fermionic objects and bosonic condensates.
Finally, the convenient parametrization of the solutions, enforced by the
inversion of the Pohlmeyer reduction, facilitates the study of the string
dispersion relation. This leads to the identification of an infinite set of
trajectories in the moduli space of solutions, where the dispersion relation
can be expressed in a closed form by means of some algebraic operations,
arbitrarily far from the infinite size limit.Comment: 39 pages, 5 figure