nLab
black brane

Context

Gravity

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The theory of gravity in 3+13+1 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.

Particularly the BPS states among the black branes in supergravity, i.e. those solutions that carry Killing spinors, include configurations that look like the strong-coupling version of the Green-Schwarz super p-branes. (Though, being extremal, these are not strictly speaking “black” solutions.)

The near-horizon geometry of these black branes is generically that of anti de Sitter spacetime. To the extent that the worldvolume theory of the branes is a superconformal QFT, this is the origin of the AdS-CFT correspondence.

Properties

Weak coupling correspondence

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.

Examples

Table of branes appearing in supergravity/string theory (for classification see at brane scan).

branein supergravitycharged under gauge fieldhas worldvolume theory
black branesupergravityhigher gauge fieldSCFT
D-branetype IIRR-fieldsuper Yang-Mills theory
(D=2n)(D = 2n)type IIA\,\,
D0-brane\,\,BFSS matrix model
D2-brane\,\,\,
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,
D8-brane\,\,
(D=2n+1)(D = 2n+1)type IIB\,\,
D(-1)-brane\,\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
D5-brane\,\,\,
D7-brane\,\,\,
D9-brane\,\,\,
(p,q)-string\,\,\,
(D25-brane)(bosonic string theory)
NS-branetype I, II, heteroticcircle n-connection\,
string\,B2-field2d SCFT
NS5-brane\,B6-fieldlittle string theory
D-brane for topological string\,
A-brane\,
B-brane\,
M-brane11D SuGra/M-theorycircle n-connection\,
M2-brane\,C3-fieldABJM theory, BLG model
M5-brane\,C6-field6d (2,0)-superconformal QFT
M9-brane/O9-planeheterotic string theory
M-wave
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane\,C6-field on G2-manifold
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d

References

Original articles include

The M5 brane? was maybe first found as a black brane of 11-dimensional supergravity (the black fivebrane) in

  • R. Gueven, Black pp-brane solutions of D=11D = 11 supergravity theory, Phys. Lett. B276 (1992) 49.

Review includes,

Further developments include

  • Gerard Clement, Dmitri Gal’tsov, Cedric Leygnac, Black branes on the linear dilaton background, Phys. Rev. D71 (2005) 084014 (arXiv:hep-th/0412321)

  • D. Gal’tsov, S. Klevtsov, D. Orlov, G. Clement, More on general pp-brane solutions, Int.J.Mod.Phys.A21:3575-3604, 2006 (arXiv:hep-th/0508070)

  • Michael Duff, Near-horizon brane scan revived, Nucl. Phys. B810:193-209, 2009 (arXiv:0804.3675)

  • Jay Armas, Joan Camps, Troels Harmark, Niels A. Obers, The Young Modulus of Black Strings and the Fine Structure of Blackfolds (arXiv:1110.4835)

Revised on March 24, 2015 21:50:33 by Urs Schreiber (90.176.239.82)