Type IINS five-branes: Non critical strings and their topological sectors

The near-horizon geometry of parallel NS5-branes is described by an exact s uperconformal 2d field theory based on K-10 = W-k(4) x M-6, with M-6 a flat 5+1 space time and W-k(4) = U(1) circle times SU(2)(k), a four dimensional background with non-trivial dilaton. The ten-dimensional "BULK" spectrum o f excitations of K-10 can be derived combining unitary representations of t he N = 4 superconformal theory of W-k(4) and M-6 in a modular-invariant way . All Bulk states are massive and belong to the long representations of the N-6 = 2 space-time supersymmetry. The NS5-brane states, propagating on M-6 , belong to the short representations of N-6 = 2. Both the bulk and the bra ne spectrum is derived using the powerful worldsheet technics of the N = 4 superconformal theories. We claim that both bulk and brane states are neces sary to well define the theory. The non abelian U(n) or SO(2n) structure of the 5-brane fields follows from the fusion coefficients appearing in the c orrelation functions involving SU(2)(k) conformal fields.