General effective actions

We investigate the structure of the most general actions with the symmetry group G, spontaneously broken down to a subgroup H. We show that the only possible terms in the Lagrangian density that, although not G invariant, yield G-invariant terms in the action, are in one to one correspondence with the generators of the fifth cohomology classes. For the special case of G=SU(N${)}_{\mathit{L}}$×SU(N${)}_{\mathit{R}}$ broken down to the diagonal subgroup H=SU(N${)}_{\mathit{V}}$, there is just one such term for N≥3, which for N=3 is the original Wess-Zumino-Witten term.