327 research outputs found
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
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
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
Instantons and Monopoles in General Abelian Gauges
A relation between the total instanton number and the quantum-numbers of
magnetic monopoles that arise in general Abelian gauges in SU(2) Yang-Mills
theory is established. The instanton number is expressed as the sum of the
`twists' of all monopoles, where the twist is related to a generalized Hopf
invariant. The origin of a stronger relation between instantons and monopoles
in the Polyakov gauge is discussed.Comment: 28 pages, 8 figures; comments added to put work into proper contex
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
Exact N-vortex solutions to the Ginzburg-Landau equations for kappa=1/sqrt(2)
The N-vortex solutions to the two-dimensional Ginzburg - Landau equations for
the kappa=1/\sqrt(2) parameter are built. The exact solutions are derived for
the vortices with large numbers of the magnetic flux quanta. The size of vortex
core is supposed to be much greater than the magnetic field penetration depth.
In this limiting case the problem is reduced to the determination of vortex
core shape. The corresponding nonlinear boundary problem is solved by means of
the methods of the theory of analytic functions.Comment: 12 pages in RevTex, 1 Postscript figur
Vortices in Ginzburg-Landau billiards
We present an analysis of the Ginzburg-Landau equations for the description
of a two-dimensional superconductor in a bounded domain. Using the properties
of a special integrability point of these equations which allows vortex
solutions, we obtain a closed expression for the energy of the superconductor.
The role of the boundary of the system is to provide a selection mechanism
for the number of vortices.
A geometrical interpretation of these results is presented and they are
applied to the analysis of the magnetization recently measured on small
superconducting disks. Problems related to the interaction and nucleation of
vortices are discussed.Comment: RevTex, 17 pages, 3 eps figure
Decomposition of meron configuration of SU(2) gauge field
For the meron configuration of the SU(2) gauge field in the four dimensional
Minkowskii spacetime, the decomposition into an isovector field \bn,
isoscalar fields and , and a U(1) gauge field is
attained by solving the consistency condition for \bn. The resulting \bn
turns out to possess two singular points, behave like a monopole-antimonopole
pair and reduce to the conventional hedgehog in a special case. The
field also possesses singular points, while and are regular
everywhere.Comment: 18 pages, 5 figures, Sec.4 rewritten. 5 refs. adde
Monopoles, Antimonopoles and Vortex Rings
We present a new class of static axially symmetric solutions of SU(2)
Yang-Mills-Higgs theory, where the Higgs field vanishes on rings centered
around the symmetry axis. Associating a magnetic dipole moment with each Higgs
vortex ring, the dipole moments add for solutions in the trivial topological
sector, whereas they cancel for magnetically charged solutions.Comment: 4 pages, 1 figur
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