5,976 research outputs found
Moduli Spaces of Abelian Vortices on Kahler Manifolds
We consider the self-dual vortex equations on a positive line bundle L --> M
over a compact Kaehler manifold of arbitrary dimension. When M is simply
connected, the moduli space of vortex solutions is a projective space. When M
is an abelian variety, the moduli space is the projectivization of the
Fourier-Mukai transform of L. We extend this description of the moduli space to
the abelian GLSM, i.e. to vortex equations with a torus gauge group acting
linearly on a complex vector space. After establishing the Hitchin-Kobayashi
correspondence appropriate for the general abelian GLSM, we give explicit
descriptions of the vortex moduli space in the case where the manifold M is
simply connected or is an abelian variety. In these examples we compute the
Kaehler class of the natural L^2-metric on the moduli space. In the simplest
cases we compute the volume and total scalar curvature of the muduli space.
Finally, we note that for abelian GLSM the vortex moduli space is a
compactification of the space of holomorphic maps from M to toric targets, just
as in the usual case of M being a Riemann surface. This leads to various
natural conjectures, for instance explicit formulae for the volume of the space
of maps CP^m --> CP^n.Comment: v2: 48 pages; significant changes; description of the vortex moduli
spaces of the GLSM extended to allow general values of the parameters, beyond
the generic values of v
Vortex equations in abelian gauged sigma-models
We consider nonlinear gauged sigma-models with Kahler domain and target. For
a special choice of potential these models admit Bogomolny (or self-duality)
equations -- the so-called vortex equations. We find the moduli space and
energy spectrum of the solutions of these equations when the gauge group is a
torus T^n, the domain is compact, and the target is C^n or CP^n. We also obtain
a large family of solutions when the target is a compact Kahler toric manifold.Comment: v2: 60 pages, more details than in CMP versio
Non-transitive maps in phase synchronization
Concepts from the Ergodic Theory are used to describe the existence of
non-transitive maps in attractors of phase synchronous chaotic systems. It is
shown that for a class of phase-coherent systems, e.g. the sinusoidally forced
Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization
implies that such maps exist. These ideas are also extended to other coupled
chaotic systems. In addition, a phase for a chaotic attractor is defined from
the tangent vector of the flow. Finally, it is discussed how these maps can be
used to real time detection of phase synchronization in experimental systems
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