#
nLab

D4-brane

Contents
This entry is about a D-brane species in string theory. For the items in the ADE-classification of name D4, see there.

### 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-dimensional 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:

$(D3 - NS5)
\stackrel{S}{\mapsto}
(D3 - D5)
\stackrel{T}{\mapsto}
(D4-D6)
\stackrel{IIA/M}{\mapsto}
(M5 - MK6)
\,.$

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-branes) on Taub-NUT ($\times S^1$). The M5-branes wrap the circle-fiber of Taub-NUT space, which shrinks to zero size at the origin (the MK6, 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 | 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 | |

**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

Last revised on March 1, 2019 at 13:37:53.
See the history of this page for a list of all contributions to it.