25,090 research outputs found
Topological objects in QCD
Topological excitations are prominent candidates for explaining
nonperturbative effects in QCD like confinement. In these lectures, I cover
both formal treatments and applications of topological objects. The typical
phenomena like BPS bounds, topology, the semiclassical approximation and chiral
fermions are introduced by virtue of kinks. Then I proceed in higher dimensions
with magnetic monopoles and instantons and special emphasis on calorons.
Analytical aspects are discussed and an overview over models based on these
objects as well as lattice results is given.Comment: 28 pages, 17 figures; Lectures given at 45th Internationale
Universitaetswochen fuer Theoretische Physik (International University School
of Theoretical Physics): Conceptual and Numerical Challenges in Femto- and
Peta-Scale Physics, Schladming, Styria, Austria, 24 Feb - 3 Mar 200
On orientations for gauge-theoretic moduli spaces
Let be a compact manifold, a real elliptic operator on , a Lie
group, a principal -bundle, and the
infinite-dimensional moduli space of all connections on modulo
gauge, as a topological stack. For each , we can
consider the twisted elliptic operator on X. This is a
continuous family of elliptic operators over the base , and so
has an orientation bundle , a principal -bundle parametrizing orientations of
KerCoker at each . An
orientation on is a trivialization .
In gauge theory one studies moduli spaces of connections
on satisfying some curvature condition, such as anti-self-dual
instantons on Riemannian 4-manifolds . Under good conditions is a smooth manifold, and orientations on pull back to
orientations on in the usual sense under the inclusion . This is important in areas such as Donaldson
theory, where one needs an orientation on to define enumerative
invariants.
We explain a package of techniques, some known and some new, for proving
orientability and constructing canonical orientations on ,
after fixing some algebro-topological information on . We use these to
construct canonical orientations on gauge theory moduli spaces, including new
results for moduli spaces of flat connections on 2- and 3-manifolds,
instantons, Kapustin-Witten and Vafa-Witten equations on 4-manifolds, and the
Haydys-Witten equations on 5-manifolds.
Two sequels arXiv:1811.02405, arXiv:1811.09658 discuss orientations in 7 and
8 dimensions.Comment: 60 pages. (v2) sections 2.3-2.5 rewritte
Colloidal interactions in two dimensional nematics
The interaction between two disks immersed in a 2D nematic is investigated
(i) analitically using the tensor order parameter formalism for the nematic
configuration around isolated disks and (ii) numerically using finite element
methods with adaptive meshing to minimize the corresponding Landau-de Gennes
free energy. For strong homeotropic anchoring, each disk generates a pair of
defects with one-half topological charge responsible for the 2D quadrupolar
interaction between the disks at large distances. At short distance, the
position of the defects may change, leading to unexpected complex interactions
with the quadrupolar repulsive interactions becoming attractive. This short
range attraction in all directions is still anisotropic. As the distance
between the disks decreases their preferred relative orientation with respect
to the far-field nematic director changes from oblique to perpendicular.Comment: 7 pages, 7 figure
String theory and the Kauffman polynomial
We propose a new, precise integrality conjecture for the colored Kauffman
polynomial of knots and links inspired by large N dualities and the structure
of topological string theory on orientifolds. According to this conjecture, the
natural knot invariant in an unoriented theory involves both the colored
Kauffman polynomial and the colored HOMFLY polynomial for composite
representations, i.e. it involves the full HOMFLY skein of the annulus. The
conjecture sheds new light on the relationship between the Kauffman and the
HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide
various non-trivial tests of the conjecture and we sketch the string theory
arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos
corrected, final version to appear in CM
Center vortex model for the infrared sector of Yang-Mills theory - Topological Susceptibility
A definition of the Pontryagin index for SU(2) center vortex world-surfaces
composed of plaquettes on a hypercubic lattice is constructed. It is used to
evaluate the topological susceptibility in a previously defined random surface
model for vortices, the parameters of which have been fixed such as to
reproduce the confinement properties of SU(2) Yang-Mills theory. A prediction
for the topological susceptibility is obtained which is compatible with
measurements of this quantity in lattice Yang-Mills theory.Comment: 13 revtex pages, 2 ps figures included via eps
Surface embedding, topology and dualization for spin networks
Spin networks are graphs derived from 3nj symbols of angular momentum. The
surface embedding, the topology and dualization of these networks are
considered. Embeddings into compact surfaces include the orientable sphere S^2
and the torus T, and the not orientable projective space P^2 and Klein's bottle
K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and
P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org
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