We present a gauge-fixed M 5-brane action: a 6-dimensional field theor
y of a self-interacting (0,2) tensor multiplet with 32 world-volume su
persymmetries. The quadratic pan of this action is shown to be invaria
nt under rigid OSp(6, 2/4) superconformal symmetry, with 16 supersymme
tries and 16 special supersymmetries. We explore a deep relation betwe
en the superconformal symmetry on the world-volume of the brane and th
e symmetry of the near horizon anti-de Sitter infinite throat geometry
of the M 5-brane in space-time. (C) 1998 Elsevier Science B.V.