Higher categorical groups and the classification of topological defects and textures
Oct 30, 2018Citations per year
Abstract: (arXiv)
Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context, these solitons are known as textures or defect sectors. In this paper, we address the problem of enumerating and describing the solitonic sectors of sigma models. We approach this problem via an algebraic topological method -- combinatorial homotopy, in which one models both spacetime and the target space with algebraic objects which are higher categorical generalizations of fundamental groups, and then counts the homomorphisms between them. We give a self-contained discussion with plenty of examples and a discussion on how our work fits in with the existing literature on higher groups in physics.Note:
- Also see companion paper arXiv:1810.12964, submitted by same authors, which has some overlap
- Higher groups
- defects and textures
- defect: topological
- energy: low
- sigma model
- algebra
- texture
- spontaneous symmetry breaking
- homotopy
- soliton
References(0)
Figures(28)
Loading ...