#
nLab

D7-brane

Contents
### Context

#### String theory

### Ingredients

### Critical string models

### Extended objects

### Topological strings

## Backgrounds

## Phenomenology

# Contents

## Idea

The *D7-brane* is the D-brane in type IIB string theory with worldvolume of dimension $7+1$, hence of codimension $10 - (7+1) = 2$. This is the prototypical *defect brane*.

In F-theory these are the degenration loci of the axio-dilaton elliptic fibration, where the discriminant $\Delta$ of the elliptic curve fibers vanishes and the fiber degenrates to the nodal curve (e.g. Sen 97, Blumenhagen 10, (11)).

## Properties

### Bound states

### Relation to other 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 | $\,$ | $\,$ |

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 | | | |

See also *F-theory*.

## References

### General

As a black brane the D7 is identified in

The Green-Schwarz sigma-model description of $(p,q)$-7-branes via cocycles on extended super Minkowski spacetimes is obtained in

- Makoto Sakaguchi, section 2 of
*IIB-Branes and New Spacetime Superalgebras*, JHEP 0004 (2000) 019 (arXiv:hep-th/9909143)

See also

In

- P. Meessen, T. Ortin,
*An $Sl(2,\mathbb{Z})$ Multiplet of Nine-Dimensional Type II Supergravity Theories* (arXiv:hep-th/9806120)

it is argued that 7-branes in type II string theory form not just a doublet, but a triplet under S-duality.

### In M-theory

A lift of D8-branes to M-theory M-branes, by generalized Scherk-Schwarz reduction, relating to D7-branes in F-theory, is proposed in:

Last revised on November 12, 2020 at 23:34:38.
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