nLab M-wave

Idea

One of the types of BPS states of 11-dimensional supergravity is a pp-gravitational wave-solution called the M-wave (Hull 1984). Survey includes Philip 2005 p. 94, Bandos 12.

Under the duality between M-theory and type IIA string theory the M-wave becomes the black D0-brane under double dimensional reduction (Bergshoeff & Townsend 1996).

The bound states of M-waves and M5-branes are argued to correspond to self-dual string instanton solutions in the 6d (2,0)-superconformal QFT worldsheet theory of the M5 (Chu & Isono 2012).

Properties

Spin structure

That the spinor-to-vector pairing on the M-wave takes values in just one of the two light rays is made fully explicit in Philip 05, p. 94

This is the pairing of chiral spinors in $D = 1 + 1$

Relation to M2-Branes at ADE-Singularities

The M-wave may intersect black M2-branes at ADE-singularities (show in BPST 09, bottom of p. 13 via boundary conditions for the BLG model/ABJM model).

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

• Chris Hull, Exact pp wave solutions of eleven-dimensional supergravity, Phys. Lett. B 139 (1984) 39 (spire)

• E. Bergshoeff, Paul Townsend, Super D-branes, Nucl.Phys. B490 (1997) 145-162 (arXiv:hep-th/9611173)

• Paul Townsend, first pages of M-Theory from its superalgebra, Cargese Lectures 1997 (arXiv:hep-th/9712004)

• 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)

• José Figueroa-O'Farrill, Joan Simón, section 2 of Supersymmetric Kaluza-Klein reductions of M-waves and MKK-monopoles, Class. Quant. Grav.19:6147-6174, 2002 (arXiv:hep-th/0208108)

• Simon Philip, Plane-wave limits and homogeneous M-theory backgrounds, PhD thesis, Edinburgh (2005) [pdf, pdf]

• Simon Philip, Penrose limits of homogeneous spaces, Journal of Geometry and Physics 56 9 (2006) 1516-1533 [doi:10.1016/j.geomphys.2005.08.002, arXiv:math/0405506]

• David Berman, Malcolm J. Perry, Ergin Sezgin, Daniel C. Thompson, Boundary Conditions for Interacting Membranes, JHEP 1004:025, 2010 (arXiv:0912.3504)

• Igor Bandos, Action for the eleven dimensional multiple M-wave system, 2012 (pdf)

• Chong-Sun Chu, Hiroshi Isono, Instanton String and M-Wave in Multiple M5-Branes System (arXiv:1305.6808, slides: pdf)

• Yoshifumi Hyakutake, Quantum M-wave and Black 0-brane, JHEP09(2014)075 (arXiv:1407.6023)

As an M-theoretic orientifold:

• Amihay Hanany, Barak Kol, section 3.3 of On Orientifolds, Discrete Torsion, Branes and M Theory, JHEP 0006 (2000) 013 (arXiv:hep-th/0003025)

• John Huerta, Hisham Sati, Urs Schreiber, Prop. 4.7 of Real ADE-equivariant (co)homotopy and Super M-branes, Comm. Math. Phys. 2019 (arXiv:1805.05987)