A tangled tale of topological fluids

We physicists love simple problems. So much so that our immediate reaction to complex puzzles is to keep staring at them until some simple picture suggests itself. Sometimes we invent mathematical versions of those pictures: For example, a mean-field theory of atomic magnetism replaces a lattice of millions of atomic spins with just one spin interacting with a field that accounts for the mean effect of all the others. The best simple ideas also carry with them another notion—universality. Phase transitions in magnets share the same essential structures with the apparently remote behavior of fluids at their critical points. Universality arises when the essential physics emerges at large length scales. It also guides theorists who “renormalize” the complex fine detail of a system into an emergent structure that has just a few parameters. A classic example is the mean-field theory of entangled polymer dynamics, one of the products of...