Types of quantum field thories
The theory of gravity in dimensions famously has black hole solutions, being the limiting configuration of a point mass gravitational source. In higher dimensional gravity, and in particular in higher dimensional supergravity, there are analogous solutions, which however are limiting configurations of a gravitational source that is supported on a line, or a surface, or a higher dimensional space. For a surface one might speak of black membrane solutions hence generally of black brane solutions.
The types of black branes that can occur in theories of supergravity that are obtained from the maximal 11-dimensional supergravity match precisely the types of D-branes and NS-branes that appear in the corresponding perturbative superstring theories.
The idea is that both these brane-phenomena are aspects of one single entity:
At low string coupling the D-brane/NS-brane description is accurate. Low string coupling implies that the coupling of gravity is weak, hence that the back-reaction of the branes on the background geometry is negligible.
At large string coupling but low energy, the effective supergravity description becomes accurate. Here the branes do back-react on the gravitational background and hence create the black brane spacetime geometry.
This duality of the brane picture is at the heart of the AdS/CFT correspondence. See there for more details.
|brane||in supergravity||charged under gauge field||has worldvolume theory|
|black brane||supergravity||higher gauge field||SCFT|
|D-brane||type II||RR-field||super Yang-Mills theory|
|D0-brane||BFSS matrix model|
|D4-brane||D=5 super Yang-Mills theory with Khovanov homology observables|
|D1-brane||2d CFT with BH entropy|
|D3-brane||N=4 D=4 super Yang-Mills theory|
|(D25-brane)||(bosonic string theory)|
|NS-brane||type I, II, heterotic||circle n-connection|
|NS5-brane||B6-field||little string theory|
|D-brane for topological string|
|M-brane||11D SuGra/M-theory||circle n-connection|
|M2-brane||C3-field||ABJM theory, BLG model|
|M5-brane||C6-field||6d (2,0)-superconformal QFT|
|M9-brane/O9-plane||heterotic string theory|
|topological M2-brane||topological M-theory||C3-field on G2-manifold|
|topological M5-brane||C6-field on G2-manifold|
|solitons on M5-brane||6d (2,0)-superconformal QFT|
|self-dual string||self-dual B-field|
|3-brane in 6d|
section 1.3 of
Recent developments include