1,032 research outputs found
Seiberg-Witten theory, monopole spectral curves and affine Toda solitons
Using Seiberg-Witten theory it is known that the dynamics of N=2
supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface. In
particular the mass formula for BPS states is given by the periods of a special
differential on this surface. In this note we point out that the surface can be
obtained from the quotient of a symmetric n-monopole spectral curve by its
symmetry group. Known results about the Seiberg-Witten curves then implies that
these monopoles are related to the Toda lattice. We make this relation explicit
via the ADHMN construction. Furthermore, in the simplest case, that of two
SU(2) monopoles, we find that the general two monopole solution is generated by
an affine Toda soliton solution of the imaginary coupled theory.Comment: uuencoded latex, 15 pages, 1 figure. To appear in Physics Letters
String-Like Lagrangians from a Generalized Geometry
This note will use Hitchin's generalized geometry and a model of axionic
gravity developed by Warren Siegel in the mid-nineties to show that the
construction of Lagrangians based on the inner product arising from the pairing
of a vector and its dual can lead naturally to the low-energy Lagrangian of the
bosonic string.Comment: Conclusions basically unchanged, but presentation streamlined
significantly. Published versio
Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds
The precise relation between Kodaira-Spencer path integral and a particular
wave function in seven dimensional quadratic field theory is established. The
special properties of three-forms in 6d, as well as Hitchin's action
functional, play an important role. The latter defines a quantum field theory
similar to Polyakov's formulation of 2d gravity; the curious analogy with
world-sheet action of bosonic string is also pointed out.Comment: 31 page
Symetric Monopoles
We discuss Bogomolny monopoles of arbitrary charge invariant
under various symmetry groups. The analysis is largely in terms of the spectral
curves, the rational maps, and the Nahm equations associated with monopoles. We
consider monopoles invariant under inversion in a plane, monopoles with cyclic
symmetry, and monopoles having the symmetry of a regular solid. We introduce
the notion of a strongly centred monopole and show that the space of such
monopoles is a geodesic submanifold of the monopole moduli space.
By solving Nahm's equations we prove the existence of a tetrahedrally
symmetric monopole of charge and an octahedrally symmetric monopole of
charge , and determine their spectral curves. Using the geodesic
approximation to analyse the scattering of monopoles with cyclic symmetry, we
discover a novel type of non-planar -monopole scattering process
Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from
the viewpoint of real Poisson geometry. We give a characterization of
holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of
Magri-Morosi and describe a double complex which computes the holomorphic
Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle
is shown to be equivalent to a matched pair of complex Lie algebroids
, in the sense of Lu. The holomorphic Lie algebroid
cohomology of is isomorphic to the cohomology of the elliptic Lie algebroid
. In the case when is a holomorphic Poisson
manifold and , such an elliptic Lie algebroid coincides with the
Dirac structure corresponding to the associated generalized complex structure
of the holomorphic Poisson manifold.Comment: 29 pages, v2: paper split into two, part 1 of 2, v3: two references
added, v4: final version to appear in International Mathematics Research
Notice
Double solid twistor spaces: the case of arbitrary signature
In a recent paper (math.DG/0701278) we constructed a series of new Moishezon
twistor spaces which is a kind of variant of the famous LeBrun twistor spaces.
In this paper we explicitly give projective models of another series of
Moishezon twistor spaces on nCP^2 for arbitrary n>2, which can be regarded as a
generalization of the twistor spaces of a 'double solid type' on 3CP^2 studied
by Kreussler, Kurke, Poon and the author. Similarly to the twistor spaces of
'double solid type' on 3CP^2, projective models of present twistor spaces have
a natural structure of double covering of a CP^2-bundle over CP^1. We
explicitly give a defining polynomial of the branch divisor of the double
covering whose restriction to fibers are degree four. If n>3 these are new
twistor spaces, to the best of the author's knowledge. We also compute the
dimension of the moduli space of these twistor spaces. Differently from
math.DG/0701278, the present investigation is based on analysis of
pluri-(half-)anticanonical systems of the twistor spaces.Comment: 30 pages, 3 figures; v2: title changed (the original title was
"Explicit construction of new Moishezon twistor spaces, II".
Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
Hidden symmetries in a covariant Hamiltonian formulation are investigated
involving gauge covariant equations of motion. The special role of the
Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce
the original phase space to another one in which the symmetries are divided
out. The reverse of the reduction procedure is done by stages performing the
unfolding of the gauge transformation followed by the Eisenhart lift in
connection with scalar potentials.Comment: 15 pages; based on a talk at QTS-7 Conference, Prague, August 7-13,
201
Compact Einstein Spaces based on Quaternionic K\"ahler Manifolds
We investigate the Einstein equation with a positive cosmological constant
for -dimensional metrics on bundles over Quaternionic K\"ahler base
manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein
equations are reduced to a set of non-linear ordinary differential equations.
We numerically find inhomogeneous compact Einstein spaces with orbifold
singularity.Comment: LaTeX 28 pages, 5 eps figure
Scalar--Flat Lorentzian Einstein--Weyl Spaces
We find all three-dimensional Einstein--Weyl spaces with the vanishing scalar
curvatureComment: 4 page
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