Coupling of M-Branes in M-Theory

Coupling of a membrane and a five-brane to the bosonic sector of D=11 supergravity is considered. The five--brane is a dyonic object which carries both an electric and a magnetic charge of the D=11 three-form gauge field $A^3$, and it couples not only to $A^3$ but also minimally couples to a six-form field $A^6$ dual to $A^3$. This implies that the 5-brane should more naturally couple to a version of D=11 supergravity where both gauge fields are present in a duality-symmetric fashion. We demonstrate how an action of duality-symmetric D=11 supergravity looks like, couple it to the five-brane and then reduce the resulting system to an action, which describes an interaction of the 5-brane with the standard D=11 supergavity.