nLab B-brane

Idea

The branes of the B-model topological string, hence a TQFT-shadow of the D-branes of the superstring. Form the derived category of coherent sheaves on the target spacetime.

Related concepts

• A-brane, homological mirror symmetry

• 2d TQFT, TCFT

• Kapustin-Witten TQFT

• Bridgeland stability condition

• quiver gauge theory

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

A classical review is

• Paul Aspinwall, D-Branes on Calabi-Yau Manifolds (arXiv:hep-th/0403166)

Further surveys of the literature include

• Kevin H. Lin, MO comment on Matrix factorization and physics, 2009

Formulation of the chain complexes of holomorphic vector bundles on the B-branes via Lie infinity-algebroid representation (see there) of the holomorphic tangent Lie algebroid is discussed in

• Aaron Bergman, Topological D-branes from Descent (arXiv:0808.0168)

The definition of a triangulated category of B-branes for the Landau-Ginzburg model via matrix factorization was proposed by Maxim Kontsevich and is written out in

• Anton Kapustin, Yi Li, D-Branes in Landau-Ginzburg Models and Algebraic Geometry (arXiv:hep-th/0210296)

• Dmitri Orlov, Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Proc. Steklov Inst. Math. 2004, no. 3 (246), 227–248 (arXiv:math/0302304)

• Dmitri OrlovDerived categories of coherent sheaves and triangulated categories of singularities, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II, 503–531, Progr. Math., 270, Birkhäuser Boston,

  Inc., Boston, MA, 2009 (arXiv:math.ag/0503632)