Related papers: Vortices and the Abel-Jacobi map
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given…
We construct an extension of the Abelian Higgs model, which consists of a complex scalar field by including an additional real, electromagnetically neutral scalar field. We couple this real scalar field to the complex scalar field via a…
We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli…
We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex.…
It is shown that abelian Higgs vortices on a hyperbolic surface $M$ can be constructed geometrically from holomorphic maps $f:M \to N$, where $N$ is also a hyperbolic surface. The fields depend on $f$ and on the metrics of $M$ and $N$. The…
The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex collision are discussed through the moduli…
Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of…
We consider the exotic vortex equations on compact Riemann surfaces. These generalise the well-known Jackiw-Pi and Ambj{\o}rn-Olesen vortex equations and arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in…
We discuss the K\"ahler quantization of moduli spaces of vortices in line bundles over compact surfaces $\Sigma$. This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schr\"odinger-Chern-Simons model. We…
We find half-BPS vortex solitons, at both weak and strong coupling, in the N=6 supersymmetric mass deformation of ABJM theory with U(N) x U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by…
We compute the p-adic Abel-Jacobi map of the product of a Hilbert modular surface and a modular curve at a null-homologous (modified) embedding of the modular curve in this product, evaluated on differentials associated to a Hilbert…
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…
We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomolgy with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural…
We compute the Euler characteristics of the moduli spaces of abelian vortices on curves with nodal and cuspidal singularities. This generalizes our previous work where only nodes were taken into account. The result we obtain is again…
The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field $k$, of arbitrary characteristic.…
We consider the Abelian-Higgs model with two complex scalar fields and arbitrary positive integer charges with the addition of a higher-order generalization of the Josephson term. The theory possesses vortices of both local and global…
We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on $\mathbbm{R}^{2}$, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in…
We study the moduli space of torsion-free G2-structures on a fixed compact manifold, and define its associated universal intermediate Jacobian J. We define the Yukawa coupling and relate it to a natural pseudo-Kahler structure on J. We…
We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type…
In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and…