#
nLab

C6-field

### Context

#### String theory

### Ingredients

### Critical string models

### Extended objects

### Topological strings

## Backgrounds

## Phenomenology

#### Differential cohomology

**differential cohomology**

## Ingredients

## Connections on bundles

## Higher abelian differential cohomology

## Higher nonabelian differential cohomology

## Fiber integration

## Application to gauge theory

# Contents

## Idea

The higher U(1)-gauge field which is the EM-dual of the C3-field in 11-dimensional supergravity. Modeled by a circle 6-bundle with connection. Couples to the M5-brane.

**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 | | | |