489 research outputs found
The Seiberg-Witten equations and the Weinstein conjecture
Let M denote a compact, oriented 3-manifold and let a denote a contact 1-form
on M. This article proves that the vector field that generates the kernel of
the 2-form da has at least one closed, integral curve.Comment: This new version has some minor correction
Saddle point solutions in Yang-Mills-dilaton theory
The coupling of a dilaton to the -Yang-Mills field leads to
interesting non-perturbative static spherically symmetric solutions which are
studied by mixed analitical and numerical methods. In the abelian sector of the
theory there are finite-energy magnetic and electric monopole solutions which
saturate the Bogomol'nyi bound. In the nonabelian sector there exist a
countable family of globally regular solutions which are purely magnetic but
have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is
bounded from above by the energy of the abelian magnetic monopole with unit
magnetic charge. The stability analysis demonstrates that the solutions are
saddle points of the energy functional with increasing number of unstable
modes. The existence and instability of these solutions are "explained" by the
Morse-theory argument recently proposed by Sudarsky and Wald.Comment: 11 page
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
Enumerative geometry of Calabi-Yau 4-folds
Gromov-Witten theory is used to define an enumerative geometry of curves in
Calabi-Yau 4-folds. The main technique is to find exact solutions to moving
multiple cover integrals. The resulting invariants are analogous to the BPS
counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold
invariants to be integers and expect a sheaf theoretic explanation.
Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including
the sextic Calabi-Yau in CP5, are also studied. A complete solution of the
Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation.Comment: 44 page
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
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
Precise Determination of Electroweak Parameters in Neutrino-Nucleon Scattering
A systematic error in the extraction of from nuclear deep
inelastic scattering of neutrinos and antineutrinos arises from higher-twist
effects arising from nuclear shadowing. We explain that these effects cause a
correction to the results of the recently reported significant deviation from
the Standard Model that is potentially as large as the deviation claimed, and
of a sign that cannot be determined without an extremely careful study of the
data set used to model the input parton distribution functions.Comment: 3pages, 0 figures, version to be published by IJMP
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
Cooling for instantons and the Wrath of Nahm
The dynamics of instantons and anti-instantons in lattice QCD can be studied
by analysing the action and topological charge of configurations as they
approach a self-dual or anti-self-dual state, i.e. a state in which S/S_0=|Q|.
We use cooling to reveal the semi-classical structure of the configurations we
study. Improved actions which eliminate discretization errors up to and
including O(a^4) are used to stabilise instantons as we cool for several
thousand sweeps. An analogously improved lattice version of the continuum
field-strength tensor is used to construct a topological charge free from
O(a^4) discretization errors. Values of the action and topological charge
obtained with these improved operators approach mutually-consistent integer
values to within a few parts in 10^4 after several hundred cooling sweeps.
Analysis of configurations with |Q| \approx 1 and |Q| \approx 2 supports the
hypothesis that a self-dual |Q|=1 configuration cannot exist on the 4-torus.Comment: 5 pages, 4 figures, talk presented at the workshop on Lattice Hadron
Physics, Cairns Australia, July 200
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
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