The Geometry of the Space of BPS Vortex-Antivortex Pairs
The Geometry of the Space of BPS Vortex-Antivortex Pairs
复制标题
BPS涡-反涡对的空间几何
DOI：
10.1007/s00220-020-03824-y
复制
发表时间：
2020
影响因子：
2.4
通讯作者：
Romão N
中科院分区：
文献类型：
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作者：
Romão N
定义在黎曼曲面上的带目标的规范σ模型支持涡旋与反涡旋稳定平衡共存的静态解。他们的模空间是一个非紧的复杂manifoldof dimensional继承了自然Kähler metricgoverning模型的低能量动力学。本文介绍了第一个详细的研究，集中在几何接近边界因子。在上，得到了接近于Dare的严格估计，这意味着它是有限体积的，并且是测地线不完全的。仔细的数值分析和一个点涡形式主义被用来推测渐近公式在小的和大的分离的限制。所有这些结果都利用了一个局部化公式，该公式用（反）涡位置处的数据表示，它是一般性的。对于任意紧空间，本文提出了一种自然紧化的规范线性sigma模型，并给出了其体积和总标量曲率的计算公式。体积公式同意建立的结果，并允许详细研究的涡旋-antivortex气体混合物的热力学。发现状态方程与的亏格无关，混合熵总是正的。
The gauged sigma model with target, defined on a Riemann surface, supports static solutions in whichvortices coexist in stable equilibrium withantivortices. Their moduli space is a noncompact complex manifoldof dimensionwhich inherits a natural Kähler metricgoverning the model’s low energy dynamics. This paper presents the first detailed study of, focussing on the geometry close to the boundary divisor. On, rigorous estimates ofclose toDare obtained which imply thathas finite volume and is geodesically incomplete. On, careful numerical analysis and a point-vortex formalism are used to conjecture asymptotic formulae forin the limits of small and large separation. All these results make use of a localization formula, expressingin terms of data at the (anti)vortex positions, which is established for general. For arbitrary compact, a natural compactification of the spaceis proposed in terms of a certain limit of gauged linear sigma models, leading to formulae for its volume and total scalar curvature. The volume formula agrees with the result established for, and allows for a detailed study of the thermodynamics of vortex-antivortex gas mixtures. It is found that the equation of state is independent of the genus of, and that the entropy of mixing is always positive.