The branes that source the RR fields of supergravity are described by the DBI action plus a CS term. I know this only from superstring considerations.

Is there a way to find this result without requiring superstring arguments?

It should, but I am not sure. I would say that one consider deformations of a static, flat brane, and asking for the deformation to be again solution of sugra equations would impose conditions on the deformations, themselves equivalent to equations of motion derived from the brane action, but I am not sure. Does someone have seen something like this in the literature?

  • $\begingroup$ Sorry, what do you mean by those branes "independently of string arguments"? Quite generally, the inner degrees of freedom for D-branes - especially things like the $U(N)$ gauge symmetry on a stack of D-branes - are derived from (open) string physics. You could imagine more general actions on branes outside string theory. At the end, they wouldn't lead to a theory that is as consistent as string theory but the reasons could be very subtle. At any rate, it's silly to try to avoid the richness of string theory and its arguments while studying objects (e.g. branes) in SUGRA. $\endgroup$ Commented Jun 20, 2013 at 8:42
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    $\begingroup$ @LubošMotl : Is it only possible to have a concept of branes in SUGRA? In 11-D SUGRA, we have a 3-form $A_3$ , but not explicitely a object charged upon this form ? $\endgroup$
    – Trimok
    Commented Jun 20, 2013 at 8:49
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    $\begingroup$ @LubošMotl: by "independently of string arguments" I mean without knowing string theory. In other words, suppose you are familiar with supergravity but not superstring theory: would you be able to find the brane action (for RR sources)? This question make sense in the realm of classical physics. Of course its not a UV-complete theory, but that's another thing. And about the silliness of the question, well, there must be a number of things that we know on branes independently from string theory, for historical reasons. I am trying to understand what are these things. $\endgroup$
    – arovai
    Commented Jun 20, 2013 at 9:06
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    $\begingroup$ @Trimok: Branes in (consistent truncations of) supergravity theories are defined in the paper by Strominger and Horowitz of 1991 (see inspirehep.net/record/29494) as some particular solution of the equations of motion. Of course there is no explicit "object" carrying the charges, but that doesn't mean that the solution doesn't exist: the equations are solved in vacuum, that is, away from the source. To the $A_3$ in 11-D sugra correspond the M2 brane solution. $\endgroup$
    – arovai
    Commented Jun 20, 2013 at 9:14

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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

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.


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