Equivalence of large-N gauge theories on a group manifold and its coset space

In 2010, Kawai, Shimasaki and one of the present authors (A.T.) showed that the large-N reduction holds on group manifolds in the sense that a large-N gauge theory on a group manifold is realized by a matrix model which is obtained by dimensionally reducing the original theory to zero dimension. In this note, generalizing the above statement, we show that a large-N gauge theory on a group manifold is equivalent to a theory which is obtained by reducing the original theory to its coset space. This is analogous to the statement of the large-N reduction on flat spaces that large-N gauge theories are independent of the volume. (C) 2018 The Author(s). Published by Elsevier B.V.