Selfdual strings and loop space Nahm equations

Understand

We give two independent arguments why the classical membrane fields should be loops.

• The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations.
• The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as $su(N)$ for any $N$) that satisfies the algebraic structure of the membrane theory.