5-BRANE EFFECTIVE ACTION IN M-THEORY

On the world-volume of an M-theory five-brane propagates a two-form wi th self-dual field strength. As this field is non-Lagrangian, there is no obvious framework for determining its partition function. An analo gous problem exists in Type IIB superstring theory for the self-dual f ive-form. The resolution of these problems and definition of the parti tion function is explained. A more complete analysis of perturbative a nomaly cancellation for M-theory five-branes is also presented, uncove ring some surprising details.