2000/10/31 by Y. Brihaye, V. Paturyan, B. M. A. G. Piette +1
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Charge (physics) #Instanton #Quantum Chromodynamics and Particle Interactions #Sigma #Sigma model #Symmetry (geometry) #Topological quantum number #Winding number #Zero (linguistics) #hep-th
paper · pdf · doi:10.1063/1.1396636
published as J.Math.Phys.42:4669-4683,2001 · Latex, 20 pages and 5 figures
arxiv created 2001/05/04 · openalex publication_date 2001/10/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a family of four-dimensional nonlinear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterized by two distinct topological charges, the Chern–Pontryagin charge of the gauge field and the degree of the map, i.e., the winding number, of the S4 field. The one-dimensional equations arising from the variation of the action density subjected to spherical symmetry are integrated numerically. Several properties of the solutions thus constructed are pointed out. The only solution with unit Chern–Pontryagin charge are the usual BPST instantons with zero S4 winding number, while solutions with unit S4 winding number have zero Chern–Pontryagin charge.