On the complete integrability of the discrete Nahm equations
Mathematical Physics
2009-10-31 v1 High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed.
Keywords
Cite
@article{arxiv.math-ph/9903017,
title = {On the complete integrability of the discrete Nahm equations},
author = {Michael K. Murray and Michael A. Singer},
journal= {arXiv preprint arXiv:math-ph/9903017},
year = {2009}
}