2017/10/31 by Ákos Nagy, Nagy, Ákos, Gonçalo Oliveira +1
Mathematics · Physics and Astronomy · #53C07 #58D27 #70S15 #83C57 #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1710.11535
openalex publication_date 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first irreducible solution of the SU (2) self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on ℝ4 were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on ℝ4, the case of the Euclidean Schwarzschild manifold has resisted many efforts for the past 40 years. By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES, we obtain: a complete description of a connected component of the moduli space of unit energy SU (2) instantons; new examples of instantons with non-integer energy (and non-trivial holonomy at infinity); a complete classification of finite energy, spherically symmetric, SU (2) instantons. As opposed to the previously known solutions, the generic instanton coming from our construction is not invariant under the full isometry group, in particular not static. Hence disproving a conjecture of Tekin.