BPS QUANTIZATION OF THE 5-BRANE

We give a unified description of all BPS states of M-theory compactifi ed on T-5 in terms of the five-brane. We compute the mass spectrum and degeneracies and find that the SO(5,5,Z) U-duality symmetry naturally arises as a T-duality by assuming that the world-volume theory of the five-brane itself is described by a string theory. We also consider t he compactification on S-1/Z(2) x T-4, and give a new explanation for its correspondence with heterotic string theory by exhibiting its dual equivalence to M-theory on K3 x S-1.