nLab M-brane

Contents

Contents

Idea

There are two types of black brane solutions in 11-dimensional supergravity, one of dimension 2+12+1, one of dimension 5+1. These are thought to correspond to a fundamental 2-brane and its EM dual, called the

The M2-brane carries electric charge under the supergravity C-field. The M5-brane is the dual magnetic charge.

Properties

Reduction to strings, D-branes and NS5-branes

from M-branes to F-branes: superstrings, D-branes and NS5-branes

M-theory on S A 1×S B 1S^1_A \times S^1_B-elliptic fibrationKK-compactification on S A 1S^1_Atype IIA string theoryT-dual KK-compactification on S B 1S^1_Btype IIB string theorygeometrize the axio-dilatonF-theory on elliptically fibered-K3 fibrationduality between F-theory and heterotic string theoryheterotic string theory on elliptic fibration
M2-brane wrapping S A 1S_A^1double dimensional reduction \mapstotype IIA superstring\mapstotype IIB superstring\mapsto\mapstoheterotic superstring
M2-brane wrapping S B 1S_B^1\mapstoD2-brane\mapstoD1-brane\mapsto
M2-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp strings and qq D2-branes\mapsto(p,q)-string\mapsto
M5-brane wrapping S A 1S_A^1double dimensional reduction \mapstoD4-brane\mapstoD5-brane\mapsto
M5-brane wrapping S B 1S_B^1\mapstoNS5-brane\mapstoNS5-brane\mapsto\mapstoNS5-brane
M5-brane wrapping pp times around S A 1S_A^1 and qq times around S B 1S_B^1\mapstopp D4-brane and qq NS5-branes\mapsto(p,q)5-brane\mapsto
M5-brane wrapping S A 1×S B 1S_A^1 \times S_B^1\mapsto\mapstoD3-brane\mapsto
KK-monopole/A-type ADE singularity (degeneration locus of S A 1S^1_A-circle fibration, Sen limit of S A 1×S B 1S^1_A \times S^1_B elliptic fibration)\mapstoD6-brane\mapstoD7-branes\mapstoA-type nodal curve cycle degeneration locus of elliptic fibration ADE 2Cycle (Sen 97, section 2)SU-gauge enhancement
KK-monopole orientifold/D-type ADE singularity\mapstoD6-brane with O6-planes\mapstoD7-branes with O7-planes\mapstoD-type nodal curve cycle degeneration locus of elliptic fibration ADE 2Cycle (Sen 97, section 3)SO-gauge enhancement
exceptional ADE-singularity\mapsto\mapsto\mapstoexceptional ADE-singularity of elliptic fibration\mapstoE6-, E7-, E8-gauge enhancement

(e.g. Johnson 97, Blumenhagen 10)

M-brane intersections

intersecting M-branes:

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

The relevant literature until 1999 is collected in

See also the references at M-theory and at M2-brane, M5-brane, M9-brane.

Discussion of some black brane-aspects of M-branes includes

  • Takeshi Sato, Section 2.3 of: Superalgebras in Many Types of M-Brane Backgrounds and Various Supersymmetric Brane Configurations, Nucl. Phys. B548 (1999) 231-257 (arXiv:hep-th/9812014)

  • David Berman, M-theory branes and their interactions, Phys. Rept. 456:89-126, 2008 (arXiv:0710.1707)

Discussion of plenty of cohomological structures involved in M-brane physics is in

Discussion of M-brane physics in terms of rational equivariant cohomotopy is in

The brane intersection laws of M-branes are discussed in

Suppposed analogy with D-brane descent in K-theory (see there):

On M-brane intersections such as M2-M5 brane bound states:

On M-brane sigma-models on exceptional generalized geometric target spacetimes:

Further references:

  • Chan Park, 2d SCFT from M-branes and its spectral network (pdf)

Last revised on July 2, 2023 at 14:33:28. See the history of this page for a list of all contributions to it.