nLab D0-brane

Idea

The D-brane of dimension $0+1$ in type IIA string theory.

Properties

The worldline theory of a collection of D0-branes is supposed to be described by the BFSS matrix model.

Properties

Nonperturbative dynamics and M-theory

The non-perturbative limit of type IIA superstring theory is supposed to be M-theory compactified on a circle.

The degree-2 RR-field that the D0-brane is charged under, with local potential 1-form $A_1$ may be understood as the KK-field induced by this compactification, hence as one part of the field of gravity in 11-dimensional supergravity.

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 96).

One aspect of the M-theory conjecture is that type IIA string theory with a condensate of D0-branes behaves like a 10-dimensional theory that develops a further circular dimension of radius scaling with the density of D0-branes. (Banks-Fischler-Shenker-Susskind 97, Polchinski 99). See also (FSS 13, section 4.2).

Bound states

bound states/brane intersections involving D0-branes:

• D0-D2 brane bound state

• D0-D4 brane bound state

Relation to other branes

The electric-magnetic dual of the D0 is the D6-brane

electric-magnetic duality of D-branes/RR-fields in type II string theory:

electric charge	magnetic charge
D0-brane	D6-brane
D1-brane	D5-brane
D2-brane	D4-brane
D3-brane	D3-brane

Related concepts

• Myers effect

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

Single (abelian) D0-branes

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

• Nissan Itzhaki, Juan Maldacena, Jacob Sonnenschein, Shimon Yankielowicz, Section 5 of: Supergravity and The Large $N$ Limit of Theories With Sixteen Supercharges, Phys. Rev. D 58, 046004 (1998) (arXiv:hep-th/9802042)

As part of the brane bouquet:

• Domenico Fiorenza, Hisham Sati, Urs Schreiber, in section 4.2 of Super Lie n-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields (arXiv:1308.5264)

Coincident (non-abelian) D0-branes

For several and (nearly) coincident D0-branes:

The BFSS matrix model:

• Tom Banks, Willy Fischler, Stephen Shenker, Leonard Susskind, M Theory As A Matrix Model: A Conjecture, Phys. Rev. D 55 (1997) [doi:10.1103/PhysRevD.55.5112, arXiv:hep-th/9610043]

• Joseph Polchinski, M-Theory and the Light Cone, Prog. Theor. Phys. Suppl. 134 (1999) 158-170 [arXiv:hep-th/9903165]

based on discussion of bound states of $N$ D0-branes in

• Edward Witten, Bound States of Strings and $p$-Branes, Nucl.Phys. B 460, 1995, 335 (arXiv:hep-th/9510135).

Extension to a non-abelian and supersymmetric DBI-action:

• Sudhakar Panda, Dmitri Sorokin, Supersymmetric and Kappa-invariant Coincident D0-Branes, JHEP 0302 (2003) 055 [arXivLhep-th/0301065, doi:10.1088/1126-6708/2003/02/055]

• Igor Bandos, Unai D. M. Sarraga, Complete nonlinear action for supersymmetric multiple D0-brane system, Phys. Rev. D 106 (2022) 066004 [doi:10.1103/PhysRevD.106.066004, arXiv:2204.05973]

• Igor Bandos, Unai D. M. Sarraga, Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions [arXiv:2212.14829]