2015/06/29 by Joseph Y C Chan, Chan, Joseph Y C
Mathematics · Physics and Astronomy · #19L47 #19L64 #39A99 #53Z05 #55R91 #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #msc:19L47 #msc:19L64 #msc:39A99 #msc:53Z05 #msc:55R91 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1506.08736
27 pages, 2 figures. Submitted. v2: Changes to presentation and remarks have been moved to a final remarks section; no change in content v3: abstract tweaked; mass numbers -p have absorbed their sign to become p
openalex publication_date 2015/06/29 · arxiv created 2015/12/02 · arxiv updated 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a paper of Braam and Austin, SU(2) magnetic monopoles in hyperbolic space H3 were shown to be the same as solutions to matrix-valued difference equations called the discrete Nahm equations. Here, I discover the (N-1)-interval discrete Nahm equations and show that their solutions are equivalent to SU(N) hyperbolic monopoles. These discrete time evolution equations on an interval feature a jump in matrix dimensions at certain points in the evolution, which are given by the mass data of the corresponding monopole. I prove the correspondence with higher rank hyperbolic monopoles using localisation and Chern characters. I then prove that the monopole is determined up to gauge transformations by its "holographic image" of U(1) fields at the asymptotic boundary of H3.