nLab M-brane

Idea

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

• M2-brane (fractional M2-brane)

• M5-brane (half M5-brane)

• MK6-brane

• MO9-brane

• M-wave

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 $S^1_A \times S^1_B$-elliptic fibration	KK-compactification on $S^1_A$	type IIA string theory	T-dual KK-compactification on $S^1_B$	type IIB string theory	geometrize the axio-dilaton	F-theory on elliptically fibered-K3 fibration	duality between F-theory and heterotic string theory	heterotic string theory on elliptic fibration
M2-brane wrapping $S_A^1$	double dimensional reduction $\mapsto$	type IIA superstring	$\mapsto$	type IIB superstring	$\mapsto$	“	$\mapsto$	heterotic superstring
M2-brane wrapping $S_B^1$	$\mapsto$	D2-brane	$\mapsto$	D1-brane	$\mapsto$	“
M2-brane wrapping $p$ times around $S_A^1$ and $q$ times around $S_B^1$	$\mapsto$	$p$ strings and $q$ D2-branes	$\mapsto$	(p,q)-string	$\mapsto$	“
M5-brane wrapping $S_A^1$	double dimensional reduction $\mapsto$	D4-brane	$\mapsto$	D5-brane	$\mapsto$	“
M5-brane wrapping $S_B^1$	$\mapsto$	NS5-brane	$\mapsto$	NS5-brane	$\mapsto$	“	$\mapsto$	NS5-brane
M5-brane wrapping $p$ times around $S_A^1$ and $q$ times around $S_B^1$	$\mapsto$	$p$ D4-brane and $q$ NS5-branes	$\mapsto$	(p,q)5-brane	$\mapsto$	“
M5-brane wrapping $S_A^1 \times S_B^1$	$\mapsto$		$\mapsto$	D3-brane	$\mapsto$	“
KK-monopole/A-type ADE singularity (degeneration locus of $S^1_A$-circle fibration, Sen limit of $S^1_A \times S^1_B$ elliptic fibration)	$\mapsto$	D6-brane	$\mapsto$	D7-branes	$\mapsto$	A-type nodal curve cycle degeneration locus of elliptic fibration (Sen 97, section 2)		SU-gauge enhancement
KK-monopole orientifold/D-type ADE singularity	$\mapsto$	D6-brane with O6-planes	$\mapsto$	D7-branes with O7-planes	$\mapsto$	D-type nodal curve cycle degeneration locus of elliptic fibration (Sen 97, section 3)		SO-gauge enhancement
exceptional ADE-singularity	$\mapsto$		$\mapsto$		$\mapsto$	exceptional ADE-singularity of elliptic fibration	$\mapsto$	E6-, E7-, E8-gauge enhancement

(e.g. Johnson 97, Blumenhagen 10)

M-brane intersections

intersecting M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound state

  • M-string, E-string

• membrane triple junction

Related concepts

• anti M-brane

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

The relevant literature until 1999 is collected in

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

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 (2008) 89-126 [arXiv:0710.1707, doi:10.1016/j.physrep.2007.10.002]

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

• Hisham Sati, Geometric and topological structures related to M-branes (2010)

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

• John Huerta, Hisham Sati, Urs Schreiber, Real ADE-equivariant (co)homotopy and Super M-branes (arXiv:1805.05987)

The brane intersection laws of M-branes are discussed in

• Eric Bergshoeff, Mees de Roo, Eduardo Eyras, Bert Janssen, Jan Pieter Schaar?, Intersections involving waves and monopoles in eleven dimensions, Class. Quantum Grav. 14 2757 [doi:0264-9381/14/10/005]

• Eric Bergshoeff, Joaquim Gomis, Paul Townsend, M-brane intersections from worldvolume superalgebras, Phys.Lett. B421 (1998) 109-118 (arXiv:hep-th/9711043)

• Paul Townsend, section 4 of M-theory from its superalgebra (arXiv:hep-th/9712004)

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

• Laurent Houart, Yolanda Lozano, Brane Descent Relations in M-theory, Phys.Lett. B 479 (2000) 299-307 [arXiv:hep-th/0001170, doi:10.1016/S0370-2693(00)00317-8]

  (non-BPS M-branes such as M8-branes)

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

• Arkady Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B 475 (19960 149-163 [arXiv:hep-th/9604035, doi:10.1016/0550-3213(96)00328-8]

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

• Yuho Sakatani, Shozo Uehara, Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry, Phys. Rev. Lett. 117 191601 (2016) [arXiv:1607.04265, talk slides]

• Yuho Sakatani, Shozo Uehara, Exceptional M-brane sigma models and $\eta$-symbols [arXiv:1712.10316]

Further references:

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