2025/04/15 by L. A. Ferreira, Ferreira, L. A., L. R. Livramento +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2504.11533
openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a generalization of the BPS Skyrme model for simple compact Lie groups G that leads to Hermitian symmetric spaces. In such a theory, the Skyrme field takes its values in G, while the remaining fields correspond to the entries of a symmetric, positive, and invertible dim G × dim G-dimensional matrix h. We also use the holomorphic map ansatz between S2 → G/H × U(1) to study the self-dual sector of the theory, which generalizes the holomorphic ansatz between S2 → CPN. This ansatz is constructed using the fact that stable harmonic maps of the two S2 spheres for compact Hermitian symmetric spaces are holomorphic or anti-holomorphic. Apart from some special cases, the self-duality equations do not fix the matrix h entirely in terms of the Skyrme field, which is completely free, as it happens in the original self-dual Skyrme model for G=SU(2). In general, the freedom of the h fields tend to grow with the dimension of G. The holomorphic ansatz enable us to construct an infinite number of exact self-dual Skyrmions for each integer value of the topological charge and for each value of N ≥ 1, in case of the CPN, and for each values of p, q≥ 1 in case of SU(p+q)/SU(p)⊗ SU(q)⊗ U(1).