251 research outputs found
Gravitating Monopole--Antimonopole Chains and Vortex Rings
We construct monopole-antimonopole chain and vortex solutions in
Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static,
axially symmetric and asymptotically flat. They are characterized by two
integers (m,n) where m is related to the polar angle and n to the azimuthal
angle. Solutions with n=1 and n=2 correspond to chains of m monopoles and
antimonopoles. Here the Higgs field vanishes at m isolated points along the
symmetry axis. Larger values of n give rise to vortex solutions, where the
Higgs field vanishes on one or more rings, centered around the symmetry axis.
When gravity is coupled to the flat space solutions, a branch of gravitating
monopole-antimonopole chain or vortex solutions arises, and merges at a maximal
value of the coupling constant with a second branch of solutions. This upper
branch has no flat space limit. Instead in the limit of vanishing coupling
constant it either connects to a Bartnik-McKinnon or generalized
Bartnik-McKinnon solution, or, for m>4, n>4, it connects to a new
Einstein-Yang-Mills solution. In this latter case further branches of solutions
appear. For small values of the coupling constant on the upper branches, the
solutions correspond to composite systems, consisting of a scaled inner
Einstein-Yang-Mills solution and an outer Yang-Mills-Higgs solution.Comment: 18 pages, 12 figures, uses revte
Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories
We review localization techniques for functional integrals which have
recently been used to perform calculations in and gain insight into the
structure of certain topological field theories and low-dimensional gauge
theories. These are the functional integral counterparts of the Mathai-Quillen
formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula
respectively. In each case, we first introduce the necessary mathematical
background (Euler classes of vector bundles, equivariant cohomology, topology
of Lie groups), and describe the finite dimensional integration formulae. We
then discuss some applications to path integrals and give an overview of the
relevant literature. The applications we deal with include supersymmetric
quantum mechanics, cohomological field theories, phase space path integrals,
and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of
Mathematical Physics Special Issue on Functional Integration (May 1995)
Laplacian modes probing gauge fields
We show that low-lying eigenmodes of the Laplace operator are suitable to
represent properties of the underlying SU(2) lattice configurations. We study
this for the case of finite temperature background fields, yet in the
confinement phase. For calorons as classical solutions put on the lattice, the
lowest mode localizes one of the constituent monopoles by a maximum and the
other one by a minimum, respectively. We introduce adjustable phase boundary
conditions in the time direction, under which the role of the monopoles in the
mode localization is interchanged. Similar hopping phenomena are observed for
thermalized configurations. We also investigate periodic and antiperiodic modes
of the adjoint Laplacian for comparison.
In the second part we introduce a new Fourier-like low-pass filter method. It
provides link variables by truncating a sum involving the Laplacian eigenmodes.
The filter not only reproduces classical structures, but also preserves the
confining potential for thermalized ensembles. We give a first characterization
of the structures emerging from this procedure.Comment: 43 pages, 26 figure
Expansion in the distance parameter for two vortices close together
Static vortices close together are studied for two different models in
2-dimen- sional Euclidean space. In a simple model for one complex field an
expansion in the parameters describing the relative position of two vortices
can be given in terms of trigonometric and exponential functions. The results
are then compared to those of the Ginzburg-Landau theory of a superconductor in
a magnetic field at the point between type-I and type-II superconductivity. For
the angular dependence a similar pattern emerges in both models. The
differences for the radial functions are studied up to third order.Comment: 14 pages, Late
On field theory quantization around instantons
With the perspective of looking for experimentally detectable physical
applications of the so-called topological embedding, a procedure recently
proposed by the author for quantizing a field theory around a non-discrete
space of classical minima (instantons, for example), the physical implications
are discussed in a ``theoretical'' framework, the ideas are collected in a
simple logical scheme and the topological version of the Ginzburg-Landau theory
of superconductivity is solved in the intermediate situation between type I and
type II superconductors.Comment: 27 pages, 5 figures, LaTe
Telescopic actions
A group action H on X is called "telescopic" if for any finitely presented
group G, there exists a subgroup H' in H such that G is isomorphic to the
fundamental group of X/H'.
We construct examples of telescopic actions on some CAT[-1] spaces, in
particular on 3 and 4-dimensional hyperbolic spaces. As applications we give
new proofs of the following statements:
(1) Aitchison's theorem: Every finitely presented group G can appear as the
fundamental group of M/J, where M is a compact 3-manifold and J is an
involution which has only isolated fixed points;
(2) Taubes' theorem: Every finitely presented group G can appear as the
fundamental group of a compact complex 3-manifold.Comment: +higher dimension
Only hybrid anyons can exist in broken symmetry phase of nonrelativistic Chern-Simons theory
We present two examples of parity-invariant Chern-Simons-Higgs
models with spontaneously broken symmetry. The models possess topological
vortex excitations. It is argued that the smallest possible flux quanta are
composites of one quantum of each type . These hybrid anyons will
dominate the statistical properties near the ground state. We analyse their
statistical interactions and find out that unlike in the case of Jackiw-Pi
solitons there is short range magnetic interaction which can lead to formation
of bound states of hybrid anyons. In addition to mutual interactions they
possess internal structure which can lead upon quantisation to discrete
spectrum of energy levels.Comment: 10 pages in plain Latex (one argument added, version accepted for
publication in Phys.Rev.D(Rapid Communications)
Notes on bordered Floer homology
This is a survey of bordered Heegaard Floer homology, an extension of the
Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is
placed on how bordered Heegaard Floer homology can be used for computations.Comment: 73 pages, 29 figures. Based on lectures at the Contact and Symplectic
Topology Summer School in Budapest, July 2012. v2: Fixed many small typo
A Monopole-Antimonopole Solution of the SU(2) Yang-Mills-Higgs Model
As shown by Taubes, in the Bogomol'nyi-Prasad-Sommerfield limit the SU(2)
Yang-Mills-Higgs model possesses smooth finite energy solutions, which do not
satisfy the first order Bogomol'nyi equations. We construct numerically such a
non-Bogomol'nyi solution, corresponding to a monopole-antimonopole pair, and
extend the construction to finite Higgs potential.Comment: 11 pages, including 4 eps figures, LaTex format using RevTe
Conservation Laws in a First Order Dynamical System of Vortices
Gauge invariant conservation laws for the linear and angular momenta are
studied in a certain 2+1 dimensional first order dynamical model of vortices in
superconductivity. In analogy with fluid vortices it is possible to express the
linear and angular momenta as low moments of vorticity. The conservation laws
are compared with those obtained in the moduli space approximation for vortex
dynamics.Comment: LaTex file, 16 page
- …