1,583 research outputs found
Cluster algebras and Poisson geometry
We introduce a Poisson variety compatible with a cluster algebra structure
and a compatible toric action on this variety. We study Poisson and topological
properties of the union of generic orbits of this toric action. In particular,
we compute the number of connected components of the union of generic toric
orbits for cluster algebras over real numbers. As a corollary we compute the
number of connected components of refined open Bruhat cells in Grassmanians
G(k,n) over real numbers.Comment: minor change
Evidence for topological nonequilibrium in magnetic configurations
We use direct numerical simulations to study the evolution, or relaxation, of
magnetic configurations to an equilibrium state. We use the full single-fluid
equations of motion for a magnetized, non-resistive, but viscous fluid; and a
Lagrangian approach is used to obtain exact solutions for the magnetic field.
As a result, the topology of the magnetic field remains unchanged, which makes
it possible to study the case of topological nonequilibrium. We find two cases
for which such nonequilibrium appears, indicating that these configurations may
develop singular current sheets.Comment: 10 pages, 5 figure
Hurwitz numbers and intersections on moduli spaces of curves
This article is an extended version of preprint math.AG/9902104. We find an
explicit formula for the number of topologically different ramified coverings
of a sphere by a genus g surface with only one complicated branching point in
terms of Hodge integrals over the moduli space of genus g curves with marked
points.Comment: 30 pages (AMSTeX). Minor typos are correcte
Compressible hydromagnetic nonlinearities in the predecoupling plasma
The adiabatic inhomogeneities of the scalar curvature lead to a compressible
flow affecting the dynamics of the hydromagnetic nonlinearities. The influence
of the plasma on the evolution of a putative magnetic field is explored with
the aim of obtaining an effective description valid for sufficiently large
scales. The bulk velocity of the plasma, computed in the framework of the
LambdaCDM scenario, feeds back into the evolution of the magnetic power spectra
leading to a (nonlocal) master equation valid in Fourier space and similar to
the ones discussed in the context of wave turbulence. Conversely, in physical
space, the magnetic power spectra obey a Schroedinger-like equation whose
effective potential depends on the large-scale curvature perturbations.
Explicit solutions are presented both in physical space and in Fourier space.
It is argued that curvature inhomogeneities, compatible with the WMAP 7yr data,
shift to lower wavenumbers the magnetic diffusivity scale.Comment: 29 page
Central Charge Anomalies in 2D Sigma Models with Twisted Mass
We discuss the central charge in supersymmetric sigma models in
two dimensions. The target space is a symmetric K\"ahler manifold, CP is
an example. The U(1) isometries allow one to introduce twisted masses in the
model. At the classical level the central charge contains Noether charges of
the U(1) isometries and a topological charge which is an integral of a total
derivative of the Killing potentials. At the quantum level the topological part
of the central charge acquires anomalous terms. A bifermion term was found
previously, using supersymmetry which relates it to the superconformal anomaly.
We present a direct calculation of this term using a number of regularizations.
We derive, for the first time, the bosonic part in the central charge anomaly.
We construct the supermultiplet of all anomalies and present its superfield
description. We also discuss a related issue of BPS solitons in the CP(1) model
and present an explicit form for the curve of marginal stability.Comment: 30 pages, 1 figure, references adde
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