315 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

### Fluctons

From the perspective of topological field theory we explore the physics
beyond instantons. We propose the fluctons as nonperturbative topological
fluctuations of vacuum, from which the self-dual domain of instantons is
attained as a particular case. Invoking the Atiyah-Singer index theorem, we
determine the dimension of the corresponding flucton moduli space, which gives
the number of degrees of freedom of the fluctons. An important consequence of
these results is that the topological phases of vacuum in non-Abelian gauge
theories are not necessarily associated with self-dual fields, but only with
smooth fields. Fluctons in different scenarios are considered, the basic
aspects of the quantum mechanical amplitude for fluctons are discussed, and the
case of gravity is discussed briefly

### Small coupling limit and multiple solutions to the Dirichlet Problem for Yang Mills connections in 4 dimensions - Part I

In this paper (Part I) and its sequels (Part II and Part III), we analyze the
structure of the space of solutions to the epsilon-Dirichlet problem for the
Yang-Mills equations on the 4-dimensional disk, for small values of the
coupling constant epsilon. These are in one-to-one correspondence with
solutions to the Dirichlet problem for the Yang Mills equations, for small
boundary data. We prove the existence of multiple solutions, and, in
particular, non minimal ones, and establish a Morse Theory for this non-compact
variational problem. In part I, we describe the problem, state the main
theorems and do the first part of the proof. This consists in transforming the
problem into a finite dimensional problem, by seeking solutions that are
approximated by the connected sum of a minimal solution with an instanton, plus
a correction term due to the boundary. An auxiliary equation is introduced that
allows us to solve the problem orthogonally to the tangent space to the space
of approximate solutions. In Part II, the finite dimensional problem is solved
via the Ljusternik-Schirelman theory, and the existence proofs are completed.
In Part III, we prove that the space of gauge equivalence classes of Sobolev
connections with prescribed boundary value is a smooth manifold, as well as
some technical lemmas used in Part I. The methods employed still work when the
4-dimensional disk is replaced by a more general compact manifold with
boundary, and SU(2) is replaced by any compact Lie group

### 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 $U(1)^{2}$ Chern-Simons theory

We present two examples of parity-invariant $[U(1)]^{2}$ 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 $(1,1)$. 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)

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