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nLab

Narain group

# Contents

## Idea

The orthogonal group $O(n,n)$ for signature $(n,n)$ is sometimes called the *Narain group* or *generalized T-duality group* for the role that it plays in T-duality of type II string theory. See also at *type II geometry*.

## Properties

### Structure group of generalized tangent bundle

For $X$ a smooth manifold, the generalized tangent bundle $T X \oplus T^* X$ has as structure group the Narain group.

### Maximal compact subgroup

The maximal compact subgroup of the Narain group is the product group $O(n) \times O(n)$. A reduction of the structure group of the generalized tangent bundle along the inclusion defines a type II geometry.

group | symbol | universal cover | symbol | higher cover | symbol |
---|

orthogonal group | $\mathrm{O}(n)$ | Pin group | $Pin(n)$ | Tring group | $Tring(n)$ |

special orthogonal group | $SO(n)$ | Spin group | $Spin(n)$ | String group | $String(n)$ |

Lorentz group | $\mathrm{O}(n,1)$ | $\,$ | $Spin(n,1)$ | $\,$ | $\,$ |

anti de Sitter group | $\mathrm{O}(n,2)$ | $\,$ | $Spin(n,2)$ | $\,$ | $\,$ |

conformal group | $\mathrm{O}(n+1,t+1)$ | $\,$ | | | |

Narain group | $O(n,n)$ | | | | |

Poincaré group | $ISO(n,1)$ | Poincaré spin group | $\widehat {ISO}(n,1)$ | $\,$ | $\,$ |

super Poincaré group | $sISO(n,1)$ | $\,$ | $\,$ | $\,$ | $\,$ |

superconformal group | | | | | |

Created on May 28, 2012 at 01:47:29.
See the history of this page for a list of all contributions to it.