8,757 research outputs found
Euler number of Instanton Moduli space and Seiberg-Witten invariants
We show that a partition function of topological twisted N=4 Yang-Mills
theory is given by Seiberg-Witten invariants on a Riemannian four manifolds
under the condition that the sum of Euler number and signature of the four
manifolds vanish. The partition function is the sum of Euler number of
instanton moduli space when it is possible to apply the vanishing theorem. And
we get a relation of Euler number labeled by the instanton number with
Seiberg-Witten invariants, too. All calculation in this paper is done without
assuming duality.Comment: LaTeX, 34 page
N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces
We study a topological Yang-Mills theory with fermionic symmetry. Our
formalism is a field theoretical interpretation of the Donaldson polynomial
invariants on compact K\"{a}hler surfaces. We also study an analogous theory on
compact oriented Riemann surfaces and briefly discuss a possible application of
the Witten's non-Abelian localization formula to the problems in the case of
compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in
Comm. Math. Phy
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, , possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.Comment: 13 pages, LaTe
On non- solutions to the Seiberg-Witten equations
We show that a previous paper of Freund describing a solution to the
Seiberg-Witten equations has a sign error rendering it a solution to a related
but different set of equations. The non- nature of Freund's solution is
discussed and clarified and we also construct a whole class of solutions to the
Seiberg-Witten equations.Comment: 8 pages, Te
The effect of prolonged simulated non- gravitational environment on mineral balance in the adult male, volume 1 Final report
Effect of prolonged bed rest with simulated weightlessness on mineral balance in male adult - Vol.
Quaternionic Monopoles
We present the simplest non-abelian version of Seiberg-Witten theory:
Quaternionic monopoles. These monopoles are associated with
Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces.
On a Kahler surface the quaternionic monopole equations decouple and lead to
the projective vortex equation for holomorphic pairs. This vortex equation
comes from a moment map and gives rise to a new complex-geometric stability
concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have
two closed subspaces, both naturally isomorphic with moduli spaces of
canonically stable holomorphic pairs. These components intersect along
Donaldsons instanton space and can be compactified with Seiberg-Witten moduli
spaces. This should provide a link between the two corresponding theories.
Notes: To appear in CMP The revised version contains more details concerning
the Uhlenbeck compactfication of the moduli space of quaternionic monopoles,
and possible applications are discussed. Attention ! Due to an ununderstandable
mistake, the duke server had replaced all the symbols "=" by "=3D" in the
tex-file of the revised version we sent on February, the 2-nd. The command
"\def{\ad}" had also been damaged !Comment: LaTeX, 35 page
Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
This paper concerns the explicit construction of extremal Kaehler metrics on
total spaces of projective bundles, which have been studied in many places. We
present a unified approach, motivated by the theory of hamiltonian 2-forms (as
introduced and studied in previous papers in the series) but this paper is
largely independent of that theory.
We obtain a characterization, on a large family of projective bundles, of
those `admissible' Kaehler classes (i.e., the ones compatible with the bundle
structure in a way we make precise) which contain an extremal Kaehler metric.
In many cases, such as on geometrically ruled surfaces, every Kaehler class is
admissible. In particular, our results complete the classification of extremal
Kaehler metrics on geometrically ruled surfaces, answering several
long-standing questions.
We also find that our characterization agrees with a notion of K-stability
for admissible Kaehler classes. Our examples and nonexistence results therefore
provide a fertile testing ground for the rapidly developing theory of stability
for projective varieties, and we discuss some of the ramifications. In
particular we obtain examples of projective varieties which are destabilized by
a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely
self-contained; partially replaces and extends math.DG/050151
Non-abelian gauge antisymmetric tensor fields
We construct the theory of non-abelian gauge antisymmetric tensor fields,
which generalize the standard Yang-MIlls fields and abelian gauge p-forms. The
corresponding gauge group acts on the space of inhomogeneous differential forms
and it is shown to be a supergroup. The wide class of generalized Chern-Simons
actions is constructed.Comment: 20 pages, Late
Topological quantum D-branes and wild embeddings from exotic smooth R^4
This is the next step of uncovering the relation between string theory and
exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges
in IIA string theory. We construct wild embeddings of spheres and relate them
to a class of topological quantum Dp-branes as well to KK theory. These branes
emerge when there are non-trivial NS-NS H-fluxes where the topological classes
are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher
dimensional -complexes into S^n correspond to Dp-branes. These wild
embeddings as constructed by using gropes are basic objects to understand
exotic smoothness as well Casson handles. Next we build C*-algebras
corresponding to the embeddings. Finally we consider topological quantum
D-branes as those which emerge from wild embeddings in question. We construct
an action for these quantum D-branes and show that the classical limit agrees
with the Born-Infeld action such that flat branes = usual embeddings.Comment: 18 pages, 1 figur
S-duality and Topological Strings
In this paper we show how S-duality of type IIB superstrings leads to an
S-duality relating A and B model topological strings on the same Calabi-Yau as
had been conjectured recently: D-instantons of the B-model correspond to
A-model perturbative amplitudes and D-instantons of the A-model capture
perturbative B-model amplitudes.
Moreover this confirms the existence of new branes in the two models.
As an application we explain the recent results concerning A-model
topological strings on Calabi-Yau and its equivalence to the statistical
mechanical model of melting crystal.Comment: 13 page
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