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B-brane
Contents
Context
String theory
Ingredients
Critical string models
Extended objects
Topological strings
Backgrounds
Phenomenology
Contents
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 .

Table of branes appearing in supergravity /string theory (for classification see at brane scan ).

brane in supergravity charge d 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

Further surveys of the literature include

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

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 Orlov Derived 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 )

Last revised on July 2, 2022 at 08:36:32.
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