SCALAR FIELD THEORY ON A KÄHLER MANIFOLD

The invariant one-loop counter terms for a class of non-polynomial complex scalar field theories are found using the background field geodesic expansion together with heat kernel methods. These theories have dynamics invariant under a group G with fields that transform linearly only under a subgroup H of G. The fields are coordinates on a complex Kählerian manifold corresponding to the coset space G/H. The technique is applied to the CPⁿ model.