Covariant Action for the Super-Five-Brane ofMTheory

We propose a complete, $d=6\mathrm{}$ covariant and kappa-symmetric, action for the $M$ theory five-brane propagating in $D=11\mathrm{}$ supergravity background. This opens a direct way of relating a wide class of super- $p$-brane solutions of string theory with the five-brane of $M$ theory, which should be useful for studying corresponding dualities and nonperturbative aspects of these theories.