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The idea of the Gauss map is unified with the concept of branes ashypersurfaces embedded into $D$-dimensional Minkowski space. The map introducesnew generalized coordinates of branes alternative to their world vectors$\mathbf{x}$ and identified with the gauge and other massless fields. In thesecoordinates the Dirac $p$-branes realize extremals of the Euler-Lagrangeequations of motion of a $(p+1)$-dimensional $SO(D-p-1)$ gauge-invariant actionin a gravitational background

Branes as solutions of gauge theories in gravitational field