Nahm's Equations and Rational Maps from ℂP¹ to ℂPⁿ

2023/10/27 by M Schult, Schult, Max
Mathematics · Physics and Astronomy · #53C07 #53C26 #81T13 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2310.18058

openalex publication_date 2023/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Nahm's equations on a bounded open interval with first order poles at the ends. By imposing further boundary conditions, extended moduli spaces are identified with spaces of rational maps from ℂP¹ to ℂPⁿ. Having the residues at one end define sums of irreducible representations of \mathfraksu(2), the dimensions of those summands correspond to holomorphic charge on the rational map side. Technical difficulties arise due to half powers in the boundary conditions. Further, a symplectomorphic identification with moduli spaces corresponding to spaces of rational maps into complete flag varieties is given.

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