We classify effective actions for Nambu-Goldstone (NG) bosons assuming
absence of anomalies. Special attention is paid to Lagrangians invariant only
up to a surface term, shown to be in a one-to-one correspondence with
Chern-Simons (CS) theories for unbroken symmetry. Without making specific
assumptions on spacetime symmetry, we give explicit expressions for these
Lagrangians, generalizing the Berry and Hopf terms in ferromagnets. Globally
well-defined matrix expressions are derived for symmetric coset spaces of
broken symmetry. The CS Lagrangians exhibit special properties, on both the
perturbative and the global topological level. The order-one CS term is
responsible for non-invariance of canonical momentum density under internal
symmetry, known as the linear momentum problem. The order-three CS term gives
rise to a novel type of interaction among NG bosons. All the CS terms are
robust against local variations of microscopic physics.Comment: 6+2 pages; v2: substantially rewritten, version to appear as a Rapid
Communication in Phys. Rev.
