9 research outputs found
New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
The application of a weak integrability concept to the Skyrme and
models in 4 dimensions is investigated. A new integrable subsystem of the
Skyrme model, allowing also for non-holomorphic solutions, is derived. This
procedure can be applied to the massive Skyrme model, as well. Moreover, an
example of a family of chiral Lagrangians providing exact, finite energy
Skyrme-like solitons with arbitrary value of the topological charge, is given.
In the case of models a tower of integrable subsystems is obtained. In
particular, in (2+1) dimensions a one-to-one correspondence between the
standard integrable submodel and the BPS sector is proved. Additionally, it is
shown that weak integrable submodels allow also for non-BPS solutions.
Geometric as well as algebraic interpretations of the integrability conditions
are also given.Comment: 23 page
On correlation functions of operators dual to classical spinning string states
We explore how to compute, classically at strong coupling, correlation
functions of local operators corresponding to classical spinning string states.
The picture we obtain is of `fattened' Witten diagrams, the evaluation of which
turns out to be surprisingly subtle and requires a modification of the naive
classical action due to a necessary projection onto appropriate wave functions.
We examine string solutions which compute the simplest case of a two-point
function and reproduce the right scaling with the anomalous dimensions
corresponding to the energies of the associated spinning string solutions. We
also describe, under some simplifying assumptions, how the spacetime dependence
of a conformal three-point correlation function arises in this setup.Comment: 27 pages, 3 figures; v2: references and comments added
K fields, compactons, and thick branes
K fields, that is, fields with a non-standard kinetic term, allow for soliton
solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions
may give rise to topological defects of the domain wall type and with finite
thickness in higher dimensions. Here we demonstrate that, for an appropriately
chosen kinetic term, propagation of linear perturbations is completely
suppressed outside the topological defect, confining the propagation of
particles inside the domain wall. On the other hand, inside the topological
defect the propagation of linear perturbations is of the standard type, in
spite of the non-standard kinetic term. Consequently, this compacton domain
wall may act like a brane of finite thickness which is embedded in a higher
dimensional space, but to which matter fields are constrained. In addition, we
find strong indications that, when gravity is taken into account, location of
gravity in the sense of Randall--Sundrum works for these compacton domain
walls. When seen from the bulk, these finite thickness branes, in fact, cannot
be distinguished from infinitely thin branes.Comment: some references and further remarks adde
Compact self-gravitating solutions of quartic (K) fields in brane cosmology
Recently we proposed that K fields, that is, fields with a non-standard
kinetic term, may provide a mechanism for the generation of thick branes, based
on the following observations. Firstly, K field theories allow for soliton
solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions
may give rise to topological defects of the domain wall type and with finite
thickness in higher dimensions. Secondly, propagation of linear perturbations
is confined inside the compacton domain wall. Further, these linear
perturbations inside the topological defect are of the standard type, in spite
of the non-standard kinetic term. Thirdly, when gravity is taken into account,
location of gravity in the sense of Randall--Sundrum works for these compacton
domain walls provided that the backreaction of gravity does not destabilize the
compacton domain wall. It is the purpose of the present paper to investigate in
detail the existence and stability of compacton domain walls in the full K
field and gravity system, using both analytical and numerical methods. We find
that the existence of the domain wall in the full system requires a correlation
between the gravitational constant and the bulk cosmological constant, which is
thoroughly analyzed.Comment: 40 pages, 18 figures, one section on brane stability added, where the
stability under fluctuations of the scalar field is demonstrate
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Iterated ϕ <sup>4</sup> kinks
A first order equation for a static kink in the presence of an
impurity is extended into an iterative scheme. At the first iteration, the
solution is the standard kink, but at the second iteration the kink impurity
generates a kink-antikink solution or a bump solution, depending on a constant
of integration. The third iterate can be a kink-antikink-kink solution or a
single kink modified by a variant of the kink's shape mode. All equations are
first order ODEs, so the nth iterate has n moduli, and it is proposed that the
moduli space could be used to model the dynamics of n kinks and antikinks.
Curiously, fixed points of the iteration are kinks