String solitons and T-duality

We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the p-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D - 4 <= p <= 6 if D >= 6 and with D - 4 <= p <= D if D < 6, transforming in the antisymmetric representation of rank m = p + 4 - D <= 4 of the T-duality symmetry SO(10 - D, 10 - D). All branes support vector multiplets except when m = 10 - D. In that case the T-duality representation splits, for D < 10, into a selfdual and anti-selfdual part, corresponding to 5-branes supporting either a vector or a tensor multiplet. In a second step we show that only certain well-defined lightlike directions in the anti-symmetric tensor representations of the T-duality group correspond to supersymmetric String Solitons. These lightlike directions define the conjugacy classes. As a by-product we show how by a straightforward procedure all solitonic fields of maximal supergravity are derived using the Kac-Moody algebra E-11.