We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual config
urations. Starting from the Type II theories compactified on K3, we analyze their toroidal dimensional reductions, showing how the resulting half-supersymmetric p-branes satisfy the wrapping rules only by taking into account all the possible higher-dimensional origins. We then consider Type II theories compactified on the orbifold T^6/(Z_2 times Z_2 ), whose massless four-dimensional theory is an N=2 supergravity. Again, the wrapping rules are obeyed only if one includes the complete orbit of the T-duality group, namely either Type IIA or Type IIB theories compactified on either the geometric or the non-geometric T-dual orbifold. Finally, we comment on the interpretation of our results in the framework of the duality between the Heterotic string compactified on K3 times T^2 and the Type II string compactified on a Calabi-Yau threefold.
We show how the brane wrapping rules, recently discovered in closed oriented string theories compactified on tori, are extended to the case of the Type IIA string compactified on K3. To this aim, a crucial role is played by the duality between this t
heory and the Heterotic string compactified on a four-dimensional torus T^4. We first show how the wrapping rules are applied to the T^4/Z_N orbifold limits of K3 by relating the D0 branes, obtained as D2 branes wrapping two-cycles, to the perturbative BPS states of the Heterotic theory on T^4. The wrapping rules are then extended to the solitonic branes of the Type IIA string, finding agreement with the analogous Heterotic states. Finally, the geometric Type IIA orbifolds are mapped, via T-duality, to non-geometric Type IIB orbifolds, where the wrapping rules are also at work and consistent with string dualities.
We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as top-forms, require a careful analysis s
ince in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear supersymmetry algebra can be introduced. We give a superspace explanation of our work. All of our results are precisely in line with the predictions of the E(11) algebra.
