70 research outputs found
Instantons, Monopoles and Toric HyperKaehler Manifolds
In this paper, the metric on the moduli space of the k=1 SU(n) periodic
instanton -or caloron- with arbitrary gauge holonomy at spatial infinity is
explicitly constructed. The metric is toric hyperKaehler and of the form
conjectured by Lee and Yi. The torus coordinates describe the residual
U(1)^{n-1} gauge invariance and the temporal position of the caloron and can
also be viewed as the phases of n monopoles that constitute the caloron. The
(1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is
performed on the space of Nahm data, which is justified by proving the
isometric property of the Nahm construction for the cases considered. An
alternative construction using the hyperKaehler quotient is also presented. The
effect of massless monopoles is briefly discussed.Comment: 30 pages, latex2
On deformation of Poisson manifolds of hydrodynamic type
We study a class of deformations of infinite-dimensional Poisson manifolds of
hydrodynamic type which are of interest in the theory of Frobenius manifolds.
We prove two results. First, we show that the second cohomology group of these
manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial.
Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous
formal deformations of the above manifolds.Comment: LaTeX file, 24 page
Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
We construct a generalization of the variations of Hodge structures on
Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0
Gromov-Witten invariantsComment: 12 pages, AMS-TeX; typos and a sign corrected, appendix added.
Submitted to IMR
Hypercomplex Integrable Systems
In this paper we study hypercomplex manifolds in four dimensions. Rather than
using an approach based on differential forms, we develop a dual approach using
vector fields. The condition on these vector fields may then be interpreted as
Lax equations, exhibiting the integrability properties of such manifolds. A
number of different field equations for such hypercomplex manifolds are
derived, one of which is in Cauchy-Kovaleskaya form which enables a formal
general solution to be given. Various other properties of the field equations
and their solutions are studied, such as their symmetry properties and the
associated hierarchy of conservation laws.Comment: Latex file, 19 page
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