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.
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Received: 26 March 1999 / Accepted: 12 October 1999
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Murray, M., Singer, M. On the Complete Integrability of the Discrete Nahm Equations. Comm Math Phys 210, 497–519 (2000). https://doi.org/10.1007/s002200050789
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DOI: https://doi.org/10.1007/s002200050789