T-duality between perturbative characters of E-8 circle times E-8 and SO(32) heterotic strings compactified on a circle

Characters of E-8 x E-8 and SO(32) heterotic strings involving the full int ernal symmetry Cartan subalgebra generators are defined after circle compac tification so that they are T-dual. The novel point, as compared with an ea rlier study of the type II case, is the appearance of Wilson lines. Using S O(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. (C) 1999 Published by Elsevier Science B.V.