2017/10/26 by Sven Bjarke Gudnason, Zhifeng Gao, Yisong Yang
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Class (philosophy) #Combinatorics #Field (mathematics) #Generalization #Geomagnetism and Paleomagnetism Studies #Geometry #Identity (music) #Infinity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Scaling #Skyrmion #Symmetry (geometry) #Theoretical and Computational Physics #Theoretical physics #Topology (electrical circuits) #Vortex #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2017.10.015
published as Nucl.Phys.B925:500-535,2017 · LaTeX: 35 pages, 1 figure; V2: comment added and typos corrected
openalex publication_date 2017/10/26 · arxiv created 2017/11/01 · arxiv updated 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.