Non-geometric orbifolds and wrapping rules

TL;DR

This paper demonstrates that counting half-supersymmetric p-branes in Type II orbifold compactifications requires considering both geometric and non-geometric T-dual configurations, extending previous wrapping rules to include all duality orbits.

Contribution

It extends the wrapping rules to account for non-geometric T-dual configurations in orbifold compactifications, clarifying their role in counting supersymmetric branes.

Findings

Wrapping rules are satisfied only when all T-duality orbits are included.

Both geometric and non-geometric configurations are essential for correct brane counting.

Results relate to dualities between heterotic and Type II string theories on different compactifications.

Abstract

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 configurations. 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.