27 research outputs found
Anyonic Bogomol'nyi Solitons in a Gauged O(3) Sigma Model
We introduce the self-dual abelian gauged sigma models where the
Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge
field. These models have quite rich structures and various limits. Our models
are found to exhibit both symmetric and broken phases of the gauge group. We
discuss the pure Chern-Simons limit in some detail and study rotationally
symmetric solitons.Comment: 14 pages, 6 Postscript figures uuencoded, written in REVTe
Instanton vibrations of the 3-Skyrmion
The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally
symmetric 3-instanton is calculated. Some small variations of the matrix
correspond to vibrations of the instanton-generated 3-Skyrmion. These
vibrations are decomposed under tetrahedral symmetry and this decomposition is
compared to previous knowledge of the 3-Skyrmion vibration spectrum.Comment: 10 pages, LaTeX, no figures, PRD version with longer introduction and
minor change
Mesons, Baryons and Waves in the Baby Skyrmion Model
We study various classical solutions of the baby-Skyrmion model in
dimensions. We point out the existence of higher energy states interpret them
as resonances of Skyrmions and anti-Skyrmions and study their decays. Most of
the discussion involves a highly exited Skyrmion-like state with winding number
one which decays into an ordinary Skyrmion and a Skyrmion-anti-Skyrmion pair.
We also study wave-like solutions of the model and show that some of such
solutions can be constructed from the solutions of the sine-Gordon equation. We
also show that the baby-Skyrmion has non-topological stationary solutions. We
study their interactions with Skyrmions.Comment: plain tex : 17 pages, 14 Postscript figures, uses epsf.te
F-term strings in the Bogomol'nyi limit are also BPS states
We derive the Bogomol'nyi equations for supersymmetric Abelian F-term cosmic
strings in four-dimensional flat space and show that, contrary to recent
statements in the literature, they are BPS states in the Bogomol'nyi limit, but
the partial breaking of supersymmetry is from N=2. The second supersymmetry is
not obvious in the N=1 formalism, so we give it explicitly in components and in
terms of a different set of N=1 chiral superfields. We also discuss the
appearance of a second supersymmetry in D-term models, and the relation to N=2
F-term models. The analysis sheds light on an apparent paradox raised by the
recent observation that D-term strings remain BPS when coupled to N=1
supergravity, whereas F-term strings break the supersymmetry completely, even
in the Bogomol'nyi limit. Finally, we comment on their semilocal extensions and
their relevance to cosmology.Comment: 11 pages; References added, minor corrections, matches published
versio
Universality and Critical Phenomena in String Defect Statistics
The idea of biased symmetries to avoid or alleviate cosmological problems
caused by the appearance of some topological defects is familiar in the context
of domain walls, where the defect statistics lend themselves naturally to a
percolation theory description, and for cosmic strings, where the proportion of
infinite strings can be varied or disappear entirely depending on the bias in
the symmetry. In this paper we measure the initial configurational statistics
of a network of string defects after a symmetry-breaking phase transition with
initial bias in the symmetry of the ground state. Using an improved algorithm,
which is useful for a more general class of self-interacting walks on an
infinite lattice, we extend the work in \cite{MHKS} to better statistics and a
different ground state manifold, namely , and explore various different
discretisations. Within the statistical errors, the critical exponents of the
Hagedorn transition are found to be quite possibly universal and identical to
the critical exponents of three-dimensional bond or site percolation. This
improves our understanding of the percolation theory description of defect
statistics after a biased phase transition, as proposed in \cite{MHKS}. We also
find strong evidence that the existence of infinite strings in the Vachaspati
Vilenkin algorithm is generic to all (string-bearing) vacuum manifolds, all
discretisations thereof, and all regular three-dimensional lattices.Comment: 62 pages, plain LaTeX, macro mathsymb.sty included, figures included.
also available on
http://starsky.pcss.maps.susx.ac.uk/groups/pt/preprints/96/96011.ps.g
Fermion zero modes in N=2 supervortices
We study the fermionic zero modes of BPS semilocal magnetic vortices in N=2
supersymmetric QED with a Fayet-Iliopoulos term and two matter hypermultiplets
of opposite charge. There is a one-parameter family of vortices with
arbitrarily wide magnetic cores. Contrary to the situation in pure
Nielsen-Olesen vortices, new zero modes are found which get their masses from
Yukawa couplings to scalar fields that do not wind and are non-zero at the
core. We clarify the relation between fermion mass and zero modes. The new zero
modes have opposite chiralities and therefore do not affect the net counting
(left minus right) of zero modes coming from index theorems but manage to evade
other index theorems in the literature that count the total number (left plus
right) of zero modes in simpler systems.Comment: 9 pages, 1 figure. Uses Revtex4. Revised version includes discussion
about the back-reaction of the fermions on the background vortex. Version to
be published in Phys. Rev.
Thermal rates for baryon and anti-baryon production
We use a form of the fluctuation-dissipation theorem to derive formulas
giving the rate of production of spin-1/2 baryons in terms of the fluctuations
of either meson or quark fields. The most general formulas do not assume
thermal or chemical equilibrium. When evaluated in a thermal ensemble we find
equilibration times on the order of 10 fm/c near the critical temperature in
QCD.Comment: 22 pages, 4 tables and 2 figures, REVTe
Measuring Cosmic Defect Correlations in Liquid Crystals
From the theory of topological defect formation proposed for the early
universe, the so called Kibble mechanism, it follows that the density
correlation functions of defects and anti-defects in a given system should be
completely determined in terms of a single length scale , the relevant
domain size. Thus, when lengths are expressed in units of , these
distributions should show universal behavior, depending only on the symmetry of
the order parameter, and space dimensions. We have verified this prediction by
analyzing the distributions of defects/anti-defects formed in the
isotropic-nematic phase transition in a thin layer of nematic liquid crystals.
Our experimental results confirm this prediction and are in reasonable
agreement with the results of numerical simulations.Comment: 15 pages, 4 figures, minor changes, few new references adde
Vortices, Instantons and Branes
The purpose of this paper is to describe a relationship between the moduli
space of vortices and the moduli space of instantons. We study charge k
vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is
isomorphic to a special Lagrangian submanifold of the moduli space of k
instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the
fixed point set of a U(1) action on the instanton moduli space which rotates
the instantons in a plane. To derive this relationship, we present a D-brane
construction in which the dynamics of vortices is described by the Higgs branch
of a U(k) gauge theory with 4 supercharges which is a truncation of the
familiar ADHM gauge theory. We further describe a moduli space construction for
semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and
vortices on the non-commutative plane. We argue that this relationship between
vortices and instantons underlies many of the quantitative similarities shared
by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure