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 TX⊕T *X has as structure group the Narain group.
The maximal compact subgroup of the Narain group is the product group O(n)×O(n). A reduction of the structure group of the generalized tangent bundle along the inclusion defines a type II geometry.