  We propose a novel approach to the brane worldvolume theory based on the
geometry of extended field theories: double field theory and exceptional field
theory. We demonstrate the effectiveness of this approach by showing that one
can reproduce the conventional bosonic string and membrane actions, and the
M5-brane action in the weak-field approximation. At a glance, the proposed
5-brane action without approximation looks different from the known M5-brane
actions, but it is consistent with the known nonlinear self-duality relation,
and it may provide a new formulation of a single M5-brane action. Actions for
exotic branes are also discussed.
