Abstract :
When the gauge groups of the two heterotic string theories are broken, over tori, to their “SO(16)×SO(16)” subgroups, the winding modes correspond to representations which are spinorial with respect to those subgroups. Globally, the two subgroups are isomorphic neither to SO(16)×SO(16) nor to each other. Any attempt to formulate the T-duality of the two theories on topologically non-trivial compactification manifolds must therefore take into account various generalizations of the “spin structure” concept. We give here a global formulation of T-duality, and show, with the aid of simple examples, that two configurations which appear to be T-dual at the local level can fail to be globally dual.
