M(atrix) theory on T⁶ and a m(atrix) theory description of KK monopoles

We discuss M(atrix) theory compactification on T⁶. This theory is described by the large N limit of the world-volume theory, of N Kaluza-Klein monopoles in eleven dimensions. We discuss the BPS states, and their arrangement in E₆ multiplets. We then propose the formulation of the world-volume theory of KK monopoles in eleven dimensions that decouples from the bulk. This is given by a large N₁ m(atrix) theory with eight supercharges, corresponding to the quantum mechanics theory of N₁ zero-branes inside the Type IIA Kaluza-Klein monopole. Various limits of the construction are considered.