nLab
Narain group

Contents

Idea

The orthogonal group O(n,n)O(n,n) for signature (n,n)(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 XX a smooth manifold, the generalized tangent bundle TXT *XT 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)×O(n)O(n) \times O(n). A reduction of the structure group of the generalized tangent bundle along the inclusion defines a type II geometry.

groupsymboluniversal coversymbolhigher coversymbol
orthogonal groupO(n)\mathrm{O}(n)Pin groupPin(n)Pin(n)Tring groupTring(n)Tring(n)
special orthogonal groupSO(n)SO(n)Spin groupSpin(n)Spin(n)String groupString(n)String(n)
Lorentz groupO(n,1)\mathrm{O}(n,1)\,Spin(n,1)Spin(n,1)\,\,
anti de Sitter groupO(n,2)\mathrm{O}(n,2)\,Spin(n,2)Spin(n,2)\,\,
Narain groupO(n,n)O(n,n)
Poincaré groupISO(n,1)ISO(n,1)Poincaré spin groupISO^(n,1)\widehat {ISO}(n,1)\,\,
super Poincaré groupsISO(n,1)sISO(n,1)\,\,\,\,
Created on May 28, 2012 01:47:29 by Urs Schreiber (82.113.99.74)