Topological duality between vortices and planar Skyrmions in BPS theories with area-preserving diffeomorphism symmetries
Topological duality between vortices and planar Skyrmions in BPS theories with area-preserving diffeomorphism symmetries
复制标题
具有保面积微分同胚对称性的 BPS 理论中涡旋和平面斯格明子之间的拓扑对偶性
DOI：
10.1103/physrevd.87.027703
复制
发表时间：
2013
影响因子：
5
通讯作者：
Adam C
中科院分区：
文献类型：
--
作者：
Adam C
Bogomol'nyi-Prasad-Sommerfield（BPS）baby Skyrme模型是baby Skyrme模型的子模型，其中非线性sigma模型项被抑制。它们的Skyrmion解决方案饱和的BPS界，相应的静态能量功能下保持面积的同态（APD）是不变的。在这里，我们表明，孤子的BPS婴儿Skyrme模型，其中携带一个非平凡的拓扑电荷（缠绕数），是对偶的BPS涡旋模型中的涡旋与拓扑电荷（涡旋数），在这个意义上，有一个映射的BPS解决方案之间的两个模型。两个模型的BPS解的能量密度是相同的。对偶性的进一步结果是，对偶BPS涡旋模型继承了BPS性质和BPS婴儿Skyrme模型的无限多对称性（APD）。最后，<?format ?>我们证明了同样的拓扑对偶性继续适用于<?format ?>模特们
The Bogomol’nyi-Prasad-Sommerfield (BPS) baby Skyrme models are submodels of baby Skyrme models, where the nonlinear sigma model term is suppressed. They have Skyrmion solutions saturating a BPS bound, and the corresponding static energy functional is invariant under area-preserving diffeomorphisms (APDs). Here we show that the solitons in the BPS baby Skyrme model, which carry a nontrivial topological charge(a winding number), are dual to vortices in a BPS vortex model with a topological charge(a vortex number), in the sense that there is a map between the BPS solutions of the two models. The corresponding energy densities of the BPS solutions of the two models are identical. A further consequence of the duality is that the dual BPS vortex models inherit the BPS property and the infinitely many symmetries (APDs) of the BPS baby Skyrme models. Finally, <?format ?>we demonstrate that the same topological duality continues to hold for thegauged versions of <?format ?>the models.