Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality

Details Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality

1998-04-13

arxiv.org/abs/hep-th/9804092v2

Nucl.Phys. B533 (1998) 25-87

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, revtex, 2 figures, minor misprints corrected, references and acknowledgments added

Scientific paper

10.1016/S0550-3213(98)00491-X

We consider six and four dimensional ${\cal N}=1$ supersymmetric orientifolds of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, and list the four dimensional ${\cal N}=1$ orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain non-perturbative sectors that are missing in the world-sheet approach. These non-perturbative sectors can be thought of as arising from D-branes wrapping various collapsed 2-cycles in the orbifold. Using these observations, we explain certain ``puzzles'' in the literature on four dimensional orientifolds. In particular, in some four dimensional orientifolds the ``naive'' tadpole cancellation conditions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadequate in these cases due to appearance of additional non-perturbative sectors. The main tools in our analyses are the map between F-theory and orientifold vacua and Type I-heterotic duality. Utilizing the consistency conditions we have found in this paper, we discuss consistent four dimensional chiral ${\cal N}=1$ Type I vacua which are non-perturbative from the heterotic viewpoint.

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