black holes in string theory




String theory


Black hole entropy

In (perturbative) string theory the Bekenstein-Hawking entropy associated to a macroscopic black hole finds an explanation as follows:

The black hole spacetime is regarded as a strongly coupled condensate of string states (closed strings, carrying gravity). One looks for a corresponding weakly-coupled background for closed strings in flat Minkowski space that is known to turn into the black hole spacetime as the string coupling is turned on. Such turn out to be certain D-brane configurations in Minkowski space: at weak coupling the D-brane does not back-react on the spacetime (since that back-reaction is mediated by closed string quanta) and so it just sits there, whereas at strong coupling it curves spacetime and may collapse to a configuration that looks like the prescribed black hole spacetime.

graphics grabbed from Ibanez-Uranga 12

Now, if the configuration has a sufficient amount of supersymmetry preserved (BPS state), then one argues (Witten 95, section 2.3) that certain observables are actually independent of the coupling constant (“protection from quantum corrections”), and accordingly these observables are the same for black holes as for the corresponding D-brane configurations in flat space, where they may be computed in string perturbation theory.

The best studied such configuration is that of D1-D5 brane bound states. For these configurations one may compute the number of BPS states (which are “protected”), hence the entropy, via the Witten genus (Strominger-Vafa 96), see at Witten genus – Relation to BPS state counting. By the above reasoning this may then be compared to the Bekenstein-Hawking entropy of the corresponding (supersymmetric) black hole. And indeed the results match the semiclassical BH-entropy to leading order and in addition provide their higher order quantum corrections. See the References below.

The T-dual version of the D1/D5-bound states are D0/D6-bound states, coming from the Kaluza-Klein monopole in 11-dimensional supergravity (e.g. Nelson 93).

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
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,D=7 super Yang-Mills theory
(D=2n+1)(D = 2n+1)type IIB\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
(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\,
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
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane\,C6-field on G2-manifold
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


A careful non-technical exposition is in

Introductions and Review

See also

Original articles

The argument that properties of BPS states are preserved as the coupling increases beyond perturbation theory and are not destroyed by non-perturbative effects originates in

The original computations of stringy black hole entropy using this argument are due to

See also

Discussion for M-theory/11-dimensional supergravity includes

Discussion relating to the Kaluza-Klein monopole includes

  • William Nelson, Kaluza-Klein Black Holes in String Theory, Phys.Rev.D49:5302-5306,1994 (arXiv:hep-th/9312058)

More recent developments include

  • Alejandra Castro, Joshua L. Davis, Per Kraus, Finn Larsen, String Theory Effects on Five-Dimensional Black Hole Physics (arXiv:0801.1863)

  • Oleg Lunin, Samir Mathur, A toy black hole S-matrix in the D1-D5 CFT (arXiv:1211.5830)

  • Alejandra Castro, Joshua M. Lapan, Alexander Maloney, Maria J. Rodriguez, Black Hole Monodromy and Conformal Field Theory (arXiv:1303.0759)

  • Francesco Benini, Paolo Milan, Black holes in 4d 𝒩=4\mathcal{N} = 4 Super-Yang-Mills (arXiv:1812.09613)

  • H. L. Dao, Parinya Karndumri, Supersymmetric AdS 5AdS_5 black holes and strings from 5D N=4N=4 gauged supergravity (arXiv:1812.10122)

Black holes in supergravity

Black holes in supergravity:

Discussion in BFSS matrix theory

Discussion of black holes via the BFSS matrix model includes the following:

Relation to topological string amplitudes

Discussion of black hole microstates via the topological string‘s Gopakumar-Vafa invariants:

Last revised on May 18, 2019 at 14:26:38. See the history of this page for a list of all contributions to it.