The Nahm Equations
What are the Nahm equations?
The Nahm equations involve four matrices, conventionally denoted
Each of these matrices - or more properly, each component of each matrix - is a function of a variable s. The Nahm equations describe how these matrices depend on s; they are ordinary differential equations in s.
The equations are
Why are the Nahm equations?
As this website hopes to show, the Nahm equations occur in a variety of different contexts, hidden in different parts of different (but interrelated) theories. They first appeared in a construction of monopoles by Werner Nahm, yet in another sense they can be thought of as a generalisation of Euler's equations for a spinning top.
Perhaps the most natural viewpoint is to view Nahm's equations as a part of the theory of self-dual connections; or maybe as part of string theory, where Nahm's equations describe configurations of extended spatial objects known as branes. One can view all these different topics as a set of islands in an archipelago of ideas - with the Nahm equations being a natural point from which to start a journey of discovery, hopping from island to island. We hope you enjoy your time on our site.