T-duality between perturbative characters of E8 ⊗ E8 and SO(32) heterotic strings compactified on a circle Original Research Article

Characters of E8 ⊗ E8 and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T-dual. The novel point, as compared with an earlier study of the type II case, is the appearance of Wilson lines. Using SO(17,1) transformations between the weight lattices reveals the existence of an intermediate theory where T-duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.