THE GEOMETRY OF THE GAUGED SIGMA-MODEL WITH WESS-ZUMINO TERM

We review the geometry and symmetries of the non-linear sigma-model in n space-time dimensions whose target space is some riemannian manifold M and which has a Wess-Zumino term corresponding to some closed n + 1 form on M. The gauging of the symmetries corresponding to the isometries of M is then considered. We find the restrictions on the geometry of the target space that are necessary for gauging to be possible, and interpret these conditions in terms of Lie algebra cohomology. For models in which there are no obstructions to gauging, we give two equivalent expressions for the gauged Wess-Zumino term. The first is a simple manifestly gauge invariant action in n + 1 dimensions while the second is an n-dimensional action which changes by a surface term under gauge transformations. Generalised descent equation techniques are formulated in a BRST superspace and used to relate the two forms of the action. The important example in which the target space is a group manifold is discussed in detail and a simple form for the gauged action is given.