Non-Abelian Berry phase, Yang-Mills instanton and USp(2k) matrix model

The non-Abelian Barry phase is computed in the T dualized quantum mechanics obtained from the USp(2k) matrix model. Integrating the fermions, we find that each of the space-time points X-nu((i)) is equipped with a pair of su( 2) Lie algebra valued pointlike singularities located at a distance m((f)) from the orientifold surface. On a four-dimensional paraboloid embedded in the five-dimensional Euclidean space, these singularities are recognized as the BPST instantons.