Narain group

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*.

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

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 | $\mathrm{O}(n,2)$ | $\,$ | $Spin(n,2)$ | $\,$ | $\,$ |

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

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

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

Created on May 28, 2012 01:47:29
by Urs Schreiber
(82.113.99.74)