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arXiv 1810.12964cond-mat.str-elhep-thmath-phmath.MP
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关于拓扑缺陷和纹理的分类

On the classification of topological defects and textures

J. P. Ang, Abhishodh Prakash

摘要:

有序相位所产生的自发破缺的连续对称性有效地描述了西格玛模型的映射到陪集空间的Goldstone模式。一个经典的问题是对西格玛模型的拓扑扇区进行分类。在简单的情况下,这可以用目标空间的同伦群来表示;但一般来说,这是一件复杂的事情-即使在二维空间中-也缺乏通用方法。在这封信中,我们介绍了一种技术,系统地分类拓扑部门的西格玛模型在不同的维度上使用的框架基础上更高的分类推广的基本组。作为示范,我们恢复了一些已知的结果,并得到了新的结果。技术和相关的数学结构在这封信中只定性描述;细节可以在我们的配套文件中找到。

英文摘要:

Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model. In simple cases, this can be expressed in terms of homotopy groups of the target space; but in general, it is a complicated affair -- even in two dimensions -- and a general method is lacking. In this letter, we introduce a technique to systematically classify topological sectors of sigma models in various dimensions using a framework based on higher categorical generalizations of the fundamental group. As a demonstration, we recover some known results and obtain new ones. The technique and relevant mathematical structures are described only qualitatively in this letter; details can be found in our companion paper.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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