#
nLab

D6-brane

### Context

#### String theory

### Ingredients

### Critical string models

### Extended objects

### Topological strings

## Backgrounds

## Phenomenology

# Contents

## Idea

The D-brane of dimension 6+1 in type IIA string theory.

## Relation to other branes

### To the KK-monopole in M-theory

The lift of the D6 to M-theory is the Kaluza-Klein monopole there (Townsend 95).

One way to understand this is as follows: the first Chern class of the M-theory circle bundle is the D0-brane degree-2 RR-field strength $R_0$. By the self-duality of the RR-fields this is the Hodge dual of the D6-brane degree-8 field strength. Now given a Kaluza-Klein monopole after removing the locus of the monopole where the circle-fiber degenerates (as in the original Dirac charge quantization argument) it is a non-degenerated circle bundle such that the integral of the 2-form $R_0$ over any 2-sphere surrounding the singular locus is non-trivial. By the usual yoga of electric-magnetic duality this integral measures the magnetic flux of a D6-brane sitting at the singular locus. For more on this see at *Kaluza-Klein monopole – Relation to the D6-brane*, and see at *M-theory lift of gauge enhancement on D6-branes*.

### To D7-branes

The T-dual of the D6 branes is the D7-brane in type IIB string theory.

### Table of branes

**from M-branes to F-branes: superstrings, D-branes and NS5-branes**

(e.g. Johnson 97, Blumenhagen 10)

## Phenomenology – Intersecting D-brane models

D6-branes are the main ingredient in type IIA string phenomenology in the guise of intersecting D-brane models, see also at string phenomenology the section *Models in type II with intersecting branes*.

**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 | $\,$ | $\,$ |

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 the Kaluza-Klein monopole in M-theory is due to

Further discussion and derivation of the Chan-Paton gauge field content on the D6 from the KK-monopole is discussed in

Revised on February 5, 2017 04:13:23
by

Urs Schreiber
(195.229.110.3)