Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender integer winding number and appear under the presence of a local Abelian symmetry. In this work we study vortices in a Maxwell-Higgs model, in which the gauge symmetry is enhanced to accommodate additional symmetries, responsible to generate localized structures to be used to constrain the vortex structure in a given region in the plane. The main aim is to examine how the vortex profile changes when it inhabits a limited region, an issue of current interest to the study of vortices at the nanometric scale.
Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
我们探讨了三维超对称杨-米尔斯理论的一维涡旋动力学，从精确配分函数的因式分解推断。在Seiberg型对偶下，三维配分函数必须保持不变，但涡动力学的变化并不是先验的。我们观察到，一维颤动的旋涡保持不变，和净效应的三维对偶映射表现为一维穿墙现象;虽然涡数可以沿着这样的对偶映射移动，一维的量子理论的行列不受影响，导致一个概念的基本涡作为基本的积木拓扑扇区。对于Aharony型对偶，特别是，其中一个必须提供额外的手征字段耦合与双方面的算子，一维壁交叉的无穷多个涡理论整齐，集体编码的三维行列式，这种额外的手征字段。因此，涡旋理论的1D穿墙编码了嵌入在3D类塞伯格对偶中的粒子-涡旋对偶。对于$\mathcal N = 4$，D膜图像被用来激发这种3d/1d连接，而对于$\mathcal N = 2$，这种3d/1d连接被用来微调否则模糊的涡旋动力学。我们还证明了一些身份的三维超对称配分函数的Aharony对偶使用这种涡壁交叉解释。
The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we find interesting dynamics of the orientational moduli. A detailed study of the inter-vortex force is provided and a phase diagram separating Abelian and non-Abelian vortex types is constructed. Some results on scatterings with non-zero impact parameter and multi-vortex collisions are included.
Superconducting materials with noncentrosymmetric lattices lacking space inversion symmetry exhibit a variety of interesting parity-breaking phenomena, including the magneto-electric effect, spin-polarized currents, helical states, and the unusual Josephson effect. We demonstrate, within a Ginzburg-Landau framework describing noncentrosymmetric superconductors with $O$ point group symmetry, that vortices can exhibit an inversion of the magnetic field at a certain distance from the vortex core. In stark contrast to conventional superconducting vortices, the magnetic-field reversal in the parity…
The class of five integrable vortex equations discussed recently by Manton is extended so it includes the relativistic BPS Chern-Simons vortices, yielding a total of nineteen vortex equations. Not all the nineteen vortex equations are integrable, but four new integrable equations are discovered and we generalize them to infinitely many sets of four integrable vortex equations, with each set denoted by its integer order $n$. Their integrability is similar to the known cases, but give rise to different (generalized) Baptista geometries, where the Baptista metric is a conformal rescaling of the b…
We consider the exotic vortex equations on compact Riemann surfaces. These generalise the well-known Jackiw-Pi and Ambjørn-Olesen vortex equations and arise as equations for Bogomolny-Prasad-Sommerfield-like configurations in nonrelativistic Chern-Simons-matter theories. We show that (exotic) vortex solutions in $U(N)$ gauge theories with a single fundamental flavour on compact Riemann surfaces can be constructed from gauged holomorphic maps into complex space forms of dimension $N$. We conjecture, with some evidence, that all such solutions arise this way. This leads us to insights regarding …
