On the complete integrability of the discrete Nahm equations

Details On the complete integrability of the discrete Nahm equations On the complete integrability of the discrete Nahm equations

1999-03-08

arxiv.org/abs/math-ph/9903017v1

Commun.Math.Phys. 210 (2000) 497-519

Physics

Mathematical Physics

Scientific paper

10.1007/s002200050789

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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