Discrete Nahm Equations for SU(N) Hyperbolic Monopoles

Autor:	Chan, Joseph Y C
Rok vydání:	2015
Předmět:	Mathematical Physics High Energy Physics - Theory Nonlinear Sciences - Exactly Solvable and Integrable Systems 53Z05 39A99 19L47 19L64 55R91
Druh dokumentu:	Working Paper
Popis:	In a paper of Braam and Austin, $\text{SU}(2)$ magnetic monopoles in hyperbolic space $H^{3}$ 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 $\text{SU}(N)$ 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 $\text{U}(1)$ fields at the asymptotic boundary of $H^{3}$. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1506.08736 Zobrazit plný text záznamu View this record from Arxiv