  The idea of the Gauss map is unified with the concept of branes as
hypersurfaces embedded into $D$-dimensional Minkowski space. The map introduces
new generalized coordinates of branes alternative to their world vectors
$\mathbf{x}$ and identified with the gauge and other massless fields. In these
coordinates the Dirac $p$-branes realize extremals of the Euler-Lagrange
equations of motion of a $(p+1)$-dimensional $SO(D-p-1)$ gauge-invariant action
in a gravitational background
