153 research outputs found
Calogero-Moser systems and Hitchin systems
We exhibit the elliptic Calogero-Moser system as a Hitchin system of
G-principal Higgs pairs. The group G, though naturally associated to any root
system, is not semi-simple. We then interpret the Lax pairs with spectral
parameter of [dP1] and [BSC1] in terms of equivariant embeddings of the Hitchin
system of G into that of GL(N).Comment: 22 pages, Plain Te
Rank 2 Integrable Systems of Prym Varieties
A correspondence between 1) rank 2 completely integrable systems of Jacobians
of algebraic curves and 2) (holomorphically) symplectic surfaces was
established in a previous paper by the first author. A more general abelian
variety that occurs as a Liouville torus of integrable systems is a prym
variety associated to a triple (S,W,V) consisting of a curve S, a finite group
W of automorphisms of S and an integral representation V. Often W is a Weyl
group of a reductive group and V is the root lattice. We establish an analogous
correspondence between: i) Rank 2 integrable systems whose Liouville tori are
generalized prym varieties Prym(S_u,W,V) of a family of curves S_u, u in U. ii)
Varieties X of dimension 1+dim(V) with a W-action and an invariant V-valued
2-form. If V is one dimensional X is a symplectic surface. We obtain a rigidity
result: When the dimension of V is at least 2, under mild additional
assumptions, all the quotient curves are isomorphic to a fixed curve C.
This rigidity result imposes considerable constraints on the variety X: X
admits a W-invariant fibration to C and the generic fiber has an affine
structure modeled after V. Examples discussed include: Hitchin systems, reduced
finite dimensional coadjoint orbits of loop algebras, and principal bundles
over elliptic K3 surfaces.Comment: 53 page
A note on monopole moduli spaces
We discuss the structure of the framed moduli space of Bogomolny monopoles
for arbitrary symmetry breaking and extend the definition of its stratification
to the case of arbitrary compact Lie groups. We show that each stratum is a
union of submanifolds for which we conjecture that the natural metric is
hyperKahler. The dimensions of the strata and of these submanifolds are
calculated, and it is found that for the latter, the dimension is always a
multiple of four.Comment: 17 pages, LaTe
New hyper-Kaehler manifolds by fixing monopoles
The construction of new hyper-Kaehler manifolds by taking the infinite
monopole mass limit of certain Bogomol'nyi-Prasad-Sommerfield monopole moduli
spaces is considered. The one-parameter family of hyperkaehler manifolds due to
Dancer is shown to be an example of such manifolds. A new family of fixed
monopole spaces is constructed. They are the moduli spaces of four SU(4)
monopoles, in the infinite mass limit of two of the monopoles. These manifolds
are shown to be nonsingular when the fixed monopole positions are distinct.Comment: Version in Phys. Rev. D. 11 pp, RevTeX, 14 Postscript diagram
Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions
For the noncommutative torus , in case of the N.C. parameter
, we construct the basis of Hilbert space {\caH}_n\thetaz_in{\cal A}_nZ_n
\times Z_n\thetagsu(n)transform covariantly by the global gauge
transformation of By acting on we establish the
isomorphism of . We embed this into the -matrix of the
elliptic Gaudin andsu_n({\cal T})D(k, u)spectral curve
describes the brane configuration, with the dynamical
variables of N.C. solitons asT^{\otimes n} / S_nthe N.C. cotangent bundle with marked points. The
eigenfunction of the Gaudin differential -operators as the
Laughli$wavefunction is solved by Bethe ansatz.Comment: 25 pages, plain latex, no figure
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
We consider 3-monopoles symmetric under inversion symmetry. We show that the
moduli space of these monopoles is an Atiyah-Hitchin submanifold of the
3-monopole moduli space. This allows what is known about 2-monopole dynamics to
be translated into results about the dynamics of 3-monopoles. Using a numerical
ADHMN construction we compute the monopole energy density at various points on
two interesting geodesics. The first is a geodesic over the two-dimensional
rounded cone submanifold corresponding to right angle scattering and the second
is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit
SO/Sp Monopoles and Branes with Orientifold 3 Plane
We study BPS monopoles in 4 dimensional N=4 SO(N) and super
Yang-Mills theories realized as the low energy effective theory of
(physical and its mirror) parallel D3 branes and an {\it Orientifold 3 plane}
with D1 branes stretched between them in type IIB string theory. Monopoles on
D3 branes give the natural understanding by embedding in SU(N) through the
constraints on both the asymptotic Higgs field (corresponding to the horizontal
positions of D3 branes) and the magnetic charges (corresponding to the number
of D1 branes) imposed by the O3 plane. The compatibility conditions of Nahm
data for monopoles for these groups can be interpreted very naturally through
the D1 branes in the presence of O3 plane.Comment: 18 pages, Latex with RevTex, 1 table, 4 figures, v2: Clarified the
introduction and improved on the supersymmetric theory on D1 branes in page 7
and 8 and this final version to appear in Phys.Rev.
SU(3) monopoles and their fields
Some aspects of the fields of charge two SU(3) monopoles with minimal
symmetry breaking are discussed. A certain class of solutions look like SU(2)
monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding
the monopoles. For large cloud size the relative moduli space metric splits as
a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2)
monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4
which corresponds to its radius and SO(3) orientation. We solve for the
long-range fields in this region, and examine the energy density and rotational
moments of inertia. The moduli space metric for these monopoles, given by
Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.
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