596 research outputs found
On the existence of minima in the Skyrme model
Well-separated Skyrme solitons of arbitrary degree attract after a suitable
relative rotation in space and iso-space, provided the orders of the solitons'
leading multipoles do not differ by more than two. I summarise the derivation
of this result, obtained jointly with Manton and Singer, and discuss to what
extent its combination with earlier results of Esteban allows one to deduce the
existence of minima of the Skyrme energy functional.Comment: 11 pages amslatex, talk given at the workshop on Integrable theories,
Solitons and Duality, Sao Paulo, July 200
Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices
The time evolution of several interacting Ginzburg-Landau vortices according
to an equation of Schroedinger type is approximated by motion on a
finite-dimensional manifold. That manifold is defined as an unstable manifold
of an auxiliary dynamical system, namely the gradient flow of the
Ginzburg-Landau energy functional. For two vortices the relevant unstable
manifold is constructed numerically and the induced dynamics is computed. The
resulting model provides a complete picture of the vortex motion for arbitrary
vortex separation, including well-separated and nearly coincident vortices.Comment: 23 pages amslatex, 5 eps figures, minor typos correcte
S-duality in SU(3) Yang-Mills Theory with Non-abelian Unbroken Gauge Group
It is observed that the magnetic charges of classical monopole solutions in
Yang-Mills-Higgs theory with non-abelian unbroken gauge group are in
one-to-one correspondence with coherent states of a dual or magnetic group
. In the spirit of the Goddard-Nuyts-Olive conjecture this
observation is interpreted as evidence for a hidden magnetic symmetry of
Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2)
is studied in detail. The action of the magnetic group on semi-classical states
is given explicitly. Investigations of dyonic excitations show that electric
and magnetic symmetry are never manifest at the same time: Non-abelian magnetic
charge obstructs the realisation of electric symmetry and vice-versa. On the
basis of this fact the charge sectors in the theory are classified and their
fusion rules are discussed. Non-abelian electric-magnetic duality is formulated
as a map between charge sectors. Coherent states obey particularly simple
fusion rules, and in the set of coherent states S-duality can be formulated as
an SL(2,Z)-mapping between sectors which leaves the fusion rules invariant.Comment: 27 pages, harvmac, amssym, one eps figure; minor misprints corrected
and title amende
The interaction energy of well-separated Skyrme solitons
We prove that the asymptotic field of a Skyrme soliton of any degree has a
non-trivial multipole expansion. It follows that every Skyrme soliton has a
well-defined leading multipole moment. We derive an expression for the linear
interaction energy of well-separated Skyrme solitons in terms of their leading
multipole moments. This expression can always be made negative by suitable
rotations of one of the Skyrme solitons in space and iso-space.We show that the
linear interaction energy dominates for large separation if the orders of the
Skyrme solitons' multipole moments differ by at most two. In that case there
are therefore always attractive forces between the Skyrme solitons.Comment: 27 pages amslate
Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
In the formulation of (2+1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincar\'e group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincar\'e transformations in a non-trivial fashion. We derive the conserved quantities associated to the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms
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