Yes, the branes of string theory are all reflected already in the underlying low-energy supergravity theories as "black branes" and particularly as the extremal black branes, the BPS solutions to the sugra equations of motion.

A much-cited lecture note on this is

• Kellogg Stelle, BPS Branes in Supergravity (arXiv:hep-th/9803116)

where for instance figure 6 on p.43 shows the brane scan of supergravity brane solutions.

But I'd recommend looking at some more recent reviews/discussions such as listed behind the above links. For instance

• Andrew Callister, Douglas Smith, Topological BPS charges in 10 and 11-dimensional supergravity, Phys. Rev. D78:065042,2008 (arXiv:0712.3235)

discusses the D-branes of type II strings as BPS solutions of type II SuGra (sections 3 and 4) and make some comments on the relation to the DBI worldvolume action.

The branes of string theory are all reflected already in the underlying low-energy supergravity theories as "black branes" and particularly as the extremal black branes, the BPS solutions to the sugra equations of motion.

A much-cited lecture note on this is

• Kellogg Stelle, BPS Branes in Supergravity (arXiv:hep-th/9803116)

where for instance figure 6 on p.43 shows the brane scan of supergravity brane solutions.

But I'd recommend looking at some more recent reviews/discussions such as listed behind the above links. For instance

• Andrew Callister, Douglas Smith, Topological BPS charges in 10 and 11-dimensional supergravity, Phys. Rev. D78:065042,2008 (arXiv:0712.3235)

discusses the D-branes of type II strings as BPS solutions of type II SuGra (sections 3 and 4) and make some comments on the relation to the DBI worldvolume action.