Fractionalization and low-energy gauge symmetries

Gauge symmetries emerge naturally in effective actions for systems where the quasiparticles have fractional quantum numbers. I discuss various ways to derive such actions, and stress that gauge fields enter both in microscopic/intermediate scale theories, and in the effective low-energy theories. As a concrete example I discuss the Chern–Simons approach to the quantum Hall system. I also illustrate the difference between a microscopic gauge symmetry and an effective low-energy gauge symmetry by constructing a U(1) lattice action similar to the Senthil–Fisher Z2 action for fractionalized insulators, and showing that they both give the same low-energy topological gauge theory.