nLab black brane

Idea

The theory of gravity in $3+1$ 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.

1/2 BPS black branes in supergravity: D-branes, F1-brane, NS5-brane, M2-brane, M5-brane

(table taken from Blumenhagen-Lüst-Theisen 13, Chapter 18.5)

The near-horizon geometry of these black branes is generically that of anti de Sitter spacetime times a sphere. 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

• black hole, black hole in string theory

• black string

• black membrane?

• black fivebrane

• string triple junction

• membrane triple junction

Related concepts

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

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
$(D = 2n)$	type IIA	$\,$	$\,$
D(-2)-brane	$\,$	$\,$
D0-brane	$\,$	$\,$	BFSS matrix model
D2-brane	$\,$	$\,$	$\,$
D4-brane	$\,$	$\,$	D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane	$\,$	$\,$	D=7 super Yang-Mills theory
D8-brane	$\,$	$\,$
$(D = 2n+1)$	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-brane	type I, II, heterotic	circle n-connection	$\,$
string	$\,$	B2-field	2d SCFT
NS5-brane	$\,$	B6-field	little string theory
D-brane for topological string			$\,$
A-brane			$\,$
B-brane			$\,$
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
M-wave
topological M2-brane	topological M-theory	C3-field on G2-manifold
topological M5-brane	$\,$	C6-field on G2-manifold
S-brane
SM2-brane, membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane	6d (2,0)-superconformal QFT
self-dual string		self-dual B-field
3-brane in 6d

References

Prehistory

• Albert Einstein, Leopold Infeld, B. Hoffmann, The gravitational equations and the problem of motion, Annals of Mathematics, Vol 39, No. 1, 1938

See also

• Wikipedia, Black hole electron

General

Original articles include

• Michael Duff, J. X. Lu, Black and super $p$-branes in diverse dimensions, Nucl.Phys. B416 (1994) 301-334 (arXiv:hep-th/9306052)

• Mike Duff, Ramzi R. Khuri, J. X. Lu, String Solitons, Phys.Rept. 259:213-326, 1995 (arXiv:hep-th/9412184)

• Michael Duff, H. Lu, Christopher Pope, The Black Branes of M-theory, Phys.Lett.B382:73-80,1996 (arXiv:hep-th/9604052)

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

• Rahmi Gueven, Black $p$-brane solutions of $D = 11$ supergravity theory, Phys. Lett. B276 (1992) 49 and in Mike Duff (ed.)The World in Eleven Dimensions_ 135-141 (spire:338203)

The observation that black $p$-branes metric for odd $p$ are completely non-singular is due to

• Gary Gibbons, Gary Horowitz, Paul Townsend, p. 15 of Higher-dimensional resolution of dilatonic black hole singularities, Class. Quant. Grav.12:297-318,1995 (arXiv:hep-th/9410073)

The suggestion that extremal/BPS state black branes are the strong coupling incarnation of fundamental branes originates in

• Chris Hull, Paul Townsend, Unity of Superstring Dualities, Nucl.Phys.B438:109-137,1995 (arXiv:hep-th/9410167)

• Edward Witten, bottom of p. 6 of String Theory Dynamics In Various Dimensions, Nucl.Phys.B443:85-126,1995 (arXiv:hep-th/9503124)

Review includes,

• Mike Duff, chapter 5 of The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory, IoP 1999 (publisher)

• Kellogg Stelle, around section 3.3. of BPS Branes in Supergravity (arXiv:hep-th/9803116)

• Ofer Aharony, S.S. Gubser, Juan Maldacena, H. Ooguri, Y. Oz, section 1.3 of Large N Field Theories, String Theory and Gravity (arXiv:hep-th/9905111)

• Thomas Mohaupt, Black holes in supergravity and string theory, Class. Quantum Grav. 17 (2000) 3429–3482 (pdf)

• Ralph Blumenhagen, Dieter Lüst, Stefan Theisen, Brane solutions in supergravity, chapter 18.5 in Basic Concepts of String Theory Part of the series Theoretical and Mathematical Physics pp 585-639 Springer 2013

and in the context of multiple M2-branes in the BLG model:

• Jonathan Bagger, Neil Lambert, Sunil Mukhi, Constantinos Papageorgakis, section 1.6 of Multiple Membranes in M-theory (arXiv:1203.3546)

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 $p$-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)