nLab
D4-brane
Context
String theory
Ingredients
Critical string models
Extended objects
Topological strings
Backgrounds
Phenomenology
Contents
Idea
The D-brane of dimension $4+1$ in type IIA string theory .

Properties
Worldvolume theory
Khovanov homology has long been expected to appear as the observables in a 4-dimension al TQFT in higher analogy of how the Jones polynomial arises as an observable in 3-dimensional Chern-Simons theory . For instance for $\Sigma : K \to K'$ a cobordism between two knots there is a natural morphism

$\Phi_\Sigma : \mathcal{K}(K) \to \mathcal{K}(K')$

between the Khovanov homologies associated to the two knots.

In (Witten11 ) it is argued, following indications in (GukovSchwarzVafa ) that this 4d TQFT is related to the worldvolume theory of the image in type IIA of D3-branes ending on NS5-branes in type IIB after one S-duality and one T-duality operation:

$(D3 - NS4)
\stackrel{S}{\mapsto}
(D3 - D5)
\stackrel{T}{\mapsto}
(D4-D6)
\,.$

Earlier indication for this had come from the observation that Chern-Simons theory is the effective background theory for the A-model 2d TCFT (see TCFT – Worldsheet and effective background theories for details).

Notice that after the above T-duality operation the $(D4-D6)$ -system wraps the $S^1$ (circle ) along which the T-duality takes place.

Lifting that configuration to 11-dimensional supergravity gives M5-branes (the erstwhile D4-brane s) on Taub-NUT? ($\times S^1$ ). The M5-branes wrap the circle-fiber of Taub-NUT, which shrinks to zero size at the origin (the location of the erstwhile D6, which is where the D4s “end”). The low-energy theory, on a stack of M5-branes, is the 6d (2,0)-susy QFT .

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 $\,$ $\,$
D0-brane $\,$ $\,$ BFSS matrix model
D2-brane $\,$ $\,$ $\,$
D4-brane $\,$ $\,$ D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane $\,$ $\,$
D8-brane $\,$ $\,$
$(D = 2n+1)$ type IIB $\,$ $\,$
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
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
topological M2-brane topological M-theory C3-field on G2-manifold
topological M5-brane $\,$ C6-field on G2-manifold
solitons on M5-brane 6d (2,0)-superconformal QFT
self-dual string self-dual B-field
3-brane in 6d

References
The relation to Khovanov homology is discussed in

Created on October 14, 2011 02:36:23
by

Urs Schreiber
(131.211.235.86)