Related papers: Abelian Higgs Vortices and Discrete Conformal Maps

We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as…

We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…

We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical…

We have constructed numerically non-Abelian vortices in an SU(2) Chern-Simons-Higgs theory with a quartic Higgs potential. We have analyzed these solutions in detail by means of improved numerical codes and found some unexpected features we…

With the aid of concrete examples, we consider the question of whether, in the presence of conformal curvature, a conformal geodesic can become trapped in smaller and smaller sets, or phrased informally: are spirals possible? We do not…

The main intention of the paper is to investigate an osculating curve under the conformal map. We obtain a sufficient condition for the conformal invariance of an osculating curve. We also find an equivalent system of a geodesic curve under…

We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…

This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the…

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…

The main aim in the current survey is to suggest models of the development of structures, such as vortices and spirals, in accretion white dwarf's binaries. Numerical methods and simulations are applied on the bases of hydrodynamic…

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten…

We consider the possibility of localizing gravity on a Nielsen-Olesen vortex in the context of the Abelian Higgs model. The vortex lives in a six-dimensional space-time with negative bulk cosmological constant. In this model we find a…

We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this…

Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…

For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…

In the present paper, we discuss gravitational relaxation models for the electroweak hierarchy problem. We show that modified gravity can naturally relax the electroweak hierarchy problem where conformal transformation provides a crucial…

We study what might be called fractional vortices, vortex configurations with the minimum winding from the viewpoint of their topological stability, but which are characterized by various notable substructures in the transverse energy…

Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the…

I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…

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.…