4,679 research outputs found
Noncommutative Vortex Solitons
We consider the noncommutative Abelian-Higgs theory and investigate general
static vortex configurations including recently found exact multi-vortex
solutions. In particular, we prove that the self-dual BPS solutions cease to
exist once the noncommutativity scale exceeds a critical value. We then study
the fluctuation spectra about the static configuration and show that the exact
non BPS solutions are unstable below the critical value. We have identified the
tachyonic degrees as well as massless moduli degrees. We then discuss the
physical meaning of the moduli degrees and construct exact time-dependent
vortex configurations where each vortex moves independently. We finally give
the moduli description of the vortices and show that the matrix nature of
moduli coordinates naturally emerges.Comment: 22 pages, 1 figure, typos corrected, a comment on the soliton size is
adde
Elliptic supertube and a Bogomol'nyi-Prasad-Sommerfield D2-brane--anti-D2-brane Pair
An exact solution, in which a D2-brane and an anti-D2-brane are connected by
an elliptically tubular D2-brane, is obtained without any junction condition.
The solution is shown to preserve one quarter of the supersymmetries of the
type-IIA Minkowski vacuum. We show that the configuration cannot be obtained by
"blowing-up" from some inhomogeneously D0-charged superstrings. The BPS bound
tells us that it is rather composed of D0-charged D2-brane-anti-D2-brane pair
and a strip of superstrings connecting them. We obtain the correction to the
charges of the string end points in the constant magnetic background.Comment: v3. 12 pages, journal version; title changed, length trimmed to fit
for Rapid Communication forma
The Moduli Space of Noncommutative Vortices
The abelian Higgs model on the noncommutative plane admits both BPS vortices
and non-BPS fluxons. After reviewing the properties of these solitons, we
discuss several new aspects of the former. We solve the Bogomoln'yi equations
perturbatively, to all orders in the inverse noncommutivity parameter, and show
that the metric on the moduli space of k vortices reduces to the computation of
the trace of a k-dimensional matrix. In the limit of large noncommutivity, we
present an explicit expression for this metric.Comment: Invited contribution to special issue of J.Math.Phys. on
"Integrability, Topological Solitons and Beyond"; 10 Pages, 1 Figure. v2:
revision of history in introductio
Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model
We present an exact collapsing solution to 2+1 gravity with a negative
cosmological constant minimally coupled to a massless scalar field, which
exhibits physical properties making it a candidate critical solution. We
discuss its global causal structure and its symmetries in relation with those
of the corresponding continously self-similar solution derived in the
case. Linear perturbations on this background lead to approximate
black hole solutions. The critical exponent is found to be .Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and
5. The value of the critical exponent has been revised to \gamma = 2/
Dynamics of BPS States in the Dirac-Born-Infeld Theory
The Dirac-Born-Infeld action with transverse scalar fields is considered to
study the dynamics of various BPS states. We first describe the characteristic
properties of the so-called 1/2 and 1/4 BPS states on the D3 brane, which can
be interpreted as F/D-strings ending on a D3-brane in Type IIB string theory
picture. We then study the response of the BPS states to low energy excitations
of massless fields on the brane, the scalar fields representing the shape
fluctuation of the brane and U(1) gauge fields describing the open string
excitations on the D-brane. This leads to an identification of interactions
between BPS states including the static potentials and the kinetic
interactions.Comment: 19 pages, 4 figures References added, Typographical errors are
correcte
Janus within Janus
We found a simple and interesting generalization of the non-supersymmetric
Janus solution in type IIB string theory. The Janus solution can be thought of
as a thick AdS_d-sliced domain wall in AdS_{d+1} space. It turns out that the
AdS_d-sliced domain wall can support its own AdS_{d-1}-sliced domain wall
within it. Indeed this pattern persists further until it reaches the
AdS_2-slice of the domain wall within self-similar AdS_{p (2<p\le d)}-sliced
domain walls. In other words the solution represents a sequence of little Janus
nested in the interface of the parent Janus according to a remarkably simple
``nesting'' rule. Via the AdS/CFT duality, the dual gauge theory description is
in general an interface CFT of higher codimensions.Comment: 15 pages, 6 figures, v2 references added. v3 eq.(3.33) correcte
Critical States in a Dissipative Sandpile Model
A directed dissipative sandpile model is studied in the two-dimension.
Numerical results indicate that the long time steady states of this model are
critical when grains are dropped only at the top or, everywhere. The critical
behaviour is mean-field like. We discuss the role of infinite avalanches of
dissipative models in periodic systems in determining the critical behaviour of
same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included
Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory
We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4
supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation
values are turned on. When only one Higgs is turned on, the Lagrangian is
purely kinetic. When all six are turned on, however, this moduli space dynamics
is augmented by five independent potential terms, each in the form of half the
squared norm of a Killing vector field on the moduli space. A generic
stationary configuration of the monopoles can be interpreted as stable non BPS
dyons, previously found as non-planar string webs connecting D3-branes. The
supersymmetric extension is also found explicitly, and gives the complete
quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry
algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR
Chaos in Sandpile Models
We have investigated the "weak chaos" exponent to see if it can be considered
as a classification parameter of different sandpile models. Simulation results
show that "weak chaos" exponent may be one of the characteristic exponents of
the attractor of \textit{deterministic} models. We have shown that the
(abelian) BTW sandpile model and the (non abelian) Zhang model posses different
"weak chaos" exponents, so they may belong to different universality classes.
We have also shown that \textit{stochasticity} destroys "weak chaos" exponents'
effectiveness so it slows down the divergence of nearby configurations. Finally
we show that getting off the critical point destroys this behavior of
deterministic models.Comment: 5 pages, 6 figure
Unified Scaling Law for Earthquakes
We show that the distribution of waiting times between earthquakes occurring
in California obeys a simple unified scaling law valid from tens of seconds to
tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly
referred to as aftershocks, is nothing but the short time limit of the general
hierarchical properties of earthquakes. There is no unique operational way of
distinguishing between main shocks and aftershocks. In the unified law, the
Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks,
and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure
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