Large N reduction on group manifolds and coset spaces

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant and SO(4) invariant manner. In addition, as an extension of the large N reduction on group manifolds, we show that large N field theories on coset spaces are also described by certain corresponding matrix models.