General Effective Actions

Abstract

We investigate the structure of the most general actions with 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 $G=SU(N{)}_L\times SU(N{)}_R$ broken down to the diagonal subgroup $H=SU(N{)}_V$, there is just one such term for $N\ge 3$, which for $N=3$ is the original Wess-Zumino-Witten term.

Comments: 15 pages, UCLA/94/TEP/25 and UTTG-12-94