Related papers: The Gromov Limit for Vortex Moduli Spaces
In this paper, we introduce a Grothendieck topology on the category of totally bounded metric spaces and develop a theory of stacks with respect to this topology. We further define the fine moduli stack of compact metric spaces and prove…
The metric on the moduli space of one abelian Higgs vortex on a surface has a natural geometrical evolution as the Bradlow parameter, which determines the vortex size, varies. It is shown by various arguments, and by calculations in special…
The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…
We demonstrate that the geometric volume of a soliton coincides with the thermodynamical volume also for field theories with higher-dimensional vacuum manifolds (e.g., for gauged scalar field theories supporting vortices or monopoles). We…
We construct a compactification of the moduli space of twisted holomorphic maps with varying complex structure and bounded energy. For a given compact symplectic manifold $X$ with a compatible complex structure and a Hamiltonian action of…
In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out…
This paper is the first input towards an open analogue of the quantum Kirwan map. We consider the adiabatic limit of the symplectic vortex equation over the unit disk for a Hamiltonian G-manifold with Lagrangian boundary condition, by…
We relate physical time with the topology of magnetic field vortices. We base ourselves on a formulation of unimodular gravity where the cosmological constant $\Lambda$ appears as the canonical dual to a variable which on-shell becomes…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
The purpose of this article is to define a capacity on certain topological measure spaces $X$ with respect to certain function spaces $V$ consisting of measurable functions. In this general theory we will not fix the space $V$ but we…
We investigate the geometry of the moduli space of N-vortices on line bundles over a closed Riemann surface of genus g > 1, in the little explored situation where 1 =< N < g. In the regime where the area of the surface is just large enough…
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of…
The Gross-Pitaevskii equation is widely used for vortex dynamics, but finite domains with hard walls or confining potentials distort bulk behavior through vortex-image effects or induced flows. Periodic boundaries reduce wall artifacts yet…
This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the…
We study BPS non-abelian semilocal vortices in U(Nc) gauge theory with Nf flavors, Nf > Nc, in the Higgs phase. The moduli space for arbitrary winding number is described using the moduli matrix formalism. We find a relation between the…
We consider vortices in the nonlocal two-dimensional Gross-Pitaevskii equation with the interaction potential having the Lorentz-shaped dependence on the relative momentum. It is shown that in the Fourier series expansion with respect to…
We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class…
Assume $(X, \omega)$ is a compact symplectic manifold with a Hamiltonian compact Lie group action and the zero in the Lie algebra is a regular value of the moment map $\mu$. We prove that a finite energy symplectic vortex exponentially…
Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…