BPS quantization of the five-brane

We give a unified description of all BPS states of M-theory compactified on T⁵ 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 the compactification on S¹/ℤ₂ × T₄, and give a new explanation for its correspondence with heterotic string theory by exhibiting its dual equivalence to M-theory on K3 × S₁.