Discrete Nahm equations for [formula omitted] hyperbolic monopoles.

In a paper of Braam and Austin, SU ( 2 ) magnetic monopoles in hyperbolic space H 3 with half-integer mass and maximal symmetry breaking, 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 of integer or half-integer mass, and maximal symmetry breaking. 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 H 3 . [ABSTRACT FROM AUTHOR]