Branes as solutions of gauge theories in gravitational field

TL;DR

This paper unifies the Gauss map with brane theory, presenting a gauge-invariant action in gravitational backgrounds where branes are hypersurfaces with generalized coordinates linked to gauge fields.

Contribution

It introduces a new formulation of branes using generalized coordinates via the Gauss map, connecting gauge fields with brane embeddings in gravitational fields.

Findings

Branes are described as extremals of a gauge-invariant action.

Generalized coordinates replace traditional world vectors.

The approach unifies brane dynamics with gauge theories in gravity.

Abstract

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