2018/10/30 by J. P. Ang, Ang, J. P., Abhishodh Prakash +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.AT #math.MP
paper · pdf · doi:10.48550/arxiv.1810.12965
Also see companion paper arXiv:1810.12964, submitted by same authors, which has some overlap
arxiv created 2018/10/30 · arxiv updated 2018/11/01
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.