nLab black brane

Contents

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.

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

(table from Blumenhagen, Lüst & Theisen 2013, 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:

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\,\,
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)(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
S-brane
SM2-brane,
membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d

References

By “black branes” one mostly refers to – generally higher-dimensional – singular solutions of theories of supergravity, referenced below at

But closely related discussion has historically been had on the possibility of identifying electrons and other fundamental particles with Kerr-Newman black holes (“black 0-branes”):

Matching KN black holes to elementary particles

On the similarity between Kerr-Newman black holes (charged and spinning “black 0-branes”) and elementary particles (sigma-model 0-branes) like electrons.

Historical precursor discussion on the possibility of geometrodynamics for fundamental particles:

Seminal observation that the gyromagnetic ratio of the Kerr-Newman black hole is 2, just as the for electron (cf. at anomalous magnetic moment):

Further discussion:

See also:

Black branes in supergravity

Original articles on black branes in supergravity (and thereby in string/M-theory):

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

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

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

Review:

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

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)

Blackfold approach

Microscopic AdS/CFT via pp-brane sigma-models

Over a decade before the modern formulation of the AdS-CFT correspondence, a candicate “microscopic” explanation was observed:

Immersing the worldvolume of a sigma-model super p p -brane (hence a “light” brane without backreaction) along the near horizon geometry (an AdS supergravity solution) of its own black brane incarnation (hence the “heavy” incarnation of the same brane, causing backreaction), its worldvolume fluctuations (after super-diffeomorphism gauge fixing) are described by the corresponding superconformal field theory (exhibited by superconformal multiplets such as “supersingletons”).

The original observation for the M2-brane:

with popular exposition in:

  • Mike Duff, Christine Sutton: The Membrane at the End of the Universe, New Scientist 118 (1988) 67-71 [inspire:268230, ISSN:0028-6664]

Further discussion including also M5-branes and D-branes:

Review:

The resulting super-conformal brane scan:

Related:

Analogous discussion for embeddings with less supersymmetry, corresponding to defects

Last revised on July 1, 2024 at 13:53:08. See the history of this page for a list of all contributions to it.