66 research outputs found
Hyperbolic Multi-Monopoles With Arbitrary Mass
On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the
limit at infinity of the norm of the Higgs field is called the mass of the
monopole. We show the existence, on hypebolic 3-space, of monopoles with given
magnetic charge and arbitrary mass. Previously, aside from charge one
monopoles, existence was known only for monopoles with integral mass (since
these arise from U(1) invariant instantons on Euclidean 4-space). The method of
proof is based on Taubes' gluing procedure, using well-separated, explicit,
charge one monopoles. The analysis is carried out in a weighted Sobolev space
and necessitates eliminating the possibility of point spectra.Comment: 20 page
Nonlinear Hodge maps
We consider maps between Riemannian manifolds in which the map is a
stationary point of the nonlinear Hodge energy. The variational equations of
this functional form a quasilinear, nondiagonal, nonuniformly elliptic system
which models certain kinds of compressible flow. Conditions are found under
which singular sets of prescribed dimension cannot occur. Various degrees of
smoothness are proven for the sonic limit, high-dimensional flow, and flow
having nonzero vorticity. The gradient flow of solutions is estimated.
Implications for other quasilinear field theories are suggested.Comment: Slightly modified and updated version; tcilatex, 32 page
Duality methods for a class of quasilinear systems
Duality methods are used to generate explicit solutions to nonlinear Hodge
systems, demonstrate the well-posedness of boundary value problems, and reveal,
via the Hodge-B\"acklund transformation, underlying symmetries among
superficially different forms of the equations.Comment: 14 page
Anti-self-dual instantons with Lagrangian boundary conditions II: Bubbling
We study bubbling phenomena of anti-self-dual instantons on \H^2\times\S,
where is a closed Riemann surface. The restriction of the instanton to
each boundary slice , z\in\pd\H^2 is required to lie in a
Lagrangian submanifold of the moduli space of flat connections over that
arises from the restrictions to the boundary of flat connections on a handle
body.
We establish an energy quantization result for sequences of instantons with
bounded energy near : Either their curvature is in fact
uniformly bounded in a neighbourhood of that slice (leading to a compactness
result) or there is a concentration of some minimum quantum of energy. We
moreover obtain a removable singularity result for instantons with finite
energy in a punctured neighbourhood of . This completes the
analytic foundations for the construction of an instanton Floer homology for
3-manifolds with boundary. This Floer homology is an intermediate object in the
program proposed by Salamon for the proof of the Atiyah-Floer conjecture for
homology-3-spheres.
In the interior case, for anti-self-instantons on , our methods
provide a new approach to the removable singularity theorem by Sibner-Sibner
for codimension 2 singularities with a holonomy condition.Comment: 44 pages. Some corrections and rearrangements in section 5: Theorem
5.1 (now 5.3) was previously stated with incorrect assumption
Construction of a New Electroweak Sphaleron
We present a self-consistent ansatz for a new sphaleron in the electroweak
standard model. The resulting field equations are solved numerically. This
sphaleron sets the height of the energy barrier for the global SU(2) anomaly.Comment: 13 pages, Latex, NIKHEF-H/93-09 (June 1993), postscript file
including figures 1 and 2 available by anonymous ftp, figure 3 available by
fax (send request to [email protected]
The topology of asymptotically locally flat gravitational instantons
In this letter we demonstrate that the intersection form of the
Hausel--Hunsicker--Mazzeo compactification of a four dimensional ALF
gravitational instanton is definite and diagonalizable over the integers if one
of the Kahler forms of the hyper-Kahler gravitational instanton metric is
exact. This leads to the topological classification of these spaces.
The proof exploits the relationship between L^2 cohomology and U(1)
anti-instantons over gravitational instantons recognized by Hitchin. We then
interprete these as reducible points in a singular SU(2) anti-instanton moduli
space over the compactification leading to the identification of its
intersection form.
This observation on the intersection form might be a useful tool in the full
geometric classification of various asymptotically locally flat gravitational
instantons.Comment: 9 pages, LaTeX, no figures; Some typos corrected, slightly differs
from the published versio
Spherically symmetric selfdual Yang-Mills instantons on curved backgrounds in all even dimensions
We present several different classes of selfdual Yang-Mills instantons in all
even d backgrounds with Euclidean signature. In d=4p+2 the only solutions we
found are on constant curvature dS and AdS backgrounds, and are evaluated in
closed form. In d=4p an interesting class of instantons are given on black hole
backgrounds. One class of solutions are (Euclidean) time-independent and
spherically symmetric in d-1 dimensions, and the other class are spherically
symmetric in all d dimensions. Some of the solutions in the former class are
evaluated numerically, all the rest being given in closed form. Analytic proofs
of existence covering all numerically evaluated solutions are given. All
instantons studied have finite action and vanishing energy momentum tensor and
do not disturb the geometry.Comment: 41 pages, 3 figure
Existence of a New Instanton in Constrained Yang-Mills-Higgs Theory
Our goal is to discover possible new 4-dimensional euclidean solutions
(instantons) in fundamental SU(2) Yang-Mills-Higgs theory, with a constraint
added to prevent collapse of the scale. We show that, most likely, there exists
one particular new constrained instanton (\Istar) with vanishing Pontryagin
index. This is based on a topological argument that involves the construction
of a non-contractible loop of 4-dimensional configurations with a certain
upperbound on the action, which we establish numerically. We expect \Istar to
be the lowest action non-trivial solution in the vacuum sector of the theory.
There also exists a related static, but unstable, solution, the new sphaleron
\Sstar. Possible applications of \Istar to the electroweak interactions include
the asymptotics of perturbation theory and the high-energy behaviour of the
total cross-section.Comment: 32 pages, Latex, NIKHEF-H/93-02 (March 1993), postscript file
including 10 figures available by anonymous ftp from nikhefh.nikhef.n
Compactness theorems of gradient Ricci solitons
In this paper, we prove the compactness theorem for gradient Ricci solitons.
Let be a sequence of compact gradient Ricci solitons
of dimension , whose curvatures have uniformly bounded
norms, whose Ricci curvatures are uniformly bounded from
below with uniformly lower bounded volume and with uniformly upper bounded
diameter, then there must exists a subsequence
converging to a compact orbifold with finitly many
isolated singularities, where is a gradient Ricci soliton metric
in an orbifold sense.Comment: 21page
- âŠ