Berryʹs connection and USp(2k) matrix model

Berryʹs connection is computed in the USp(2k) matrix model. In T dualized quantum mechanics, the Berry phase exhibits a residual interaction taking place at a distance m(f) from the orientifold surface via the integration of the fermions in the fundamental representation. This is interpreted as a coupling of the magnetic D2 with the electric D4 branes. We make a comment on the Berry phase associated with the 6D nonabelian gauge anomaly whose cancellation selects the number of flavours nf=16.