We study novel type IIB compactifications on the T 6 /Z 2 orientifold. This geometry arises in the T-dual description of Type I theory on T 6 , and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel the RR tadpoles either partially or fully by turning on three-form flux in the compact geometry. The resulting (super)potential for moduli is calculable. We demonstrate that one can find many examples of N = 1 supersymmetric vacua with greatly reduced numbers of moduli in this system. A few examples with N > 1 supersymmetry or complete supersymmetry breaking are also discussed. January 2002 1 skachru@stanford.edu 2 mschulz@stanford.edu 3 sandip@tifr.res.in

We discuss maximally symmetric curved deformations of the flat domain wall solutions of five-dimensional dilaton gravity that appeared in a recent approach to the cosmological constant problem. By analyzing the bulk field configurations and the boundary conditions at a four-dimensional maximally symmetric curved domain wall, we obtain constraints on such solutions. For a special dilaton coupling to the brane tension that appeared in recent works, we find no curved deformations, confirming and extending slightly a result of Arkani-Hamed et al. which was argued using a Z 2 symmetry of the solution. For more general dilaton-dependent brane tension, we find that the curvature is bounded by the Kaluza-Klein scale in the fifth dimension.

We present Poincare invariant domain wall ("3-brane") solutions to some 5-dimensional effective theories which can arise naturally in string theory. In particular, we find theories where Poincare invariant solutions exist for arbitrary values of the brane tension, for certain restricted forms of the bulk interactions. We describe examples in string theory where it would be natural for the quantum corrections to the tension of the brane (arising from quantum fluctuations of modes with support on the brane) to maintain the required form of the action. In such cases, the Poincare invariant solutions persist in the presence of these quantum corrections to the brane tension, so that no 4d cosmological constant is generated by these modes.

We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non CalabiYau spaces in the presence of background NS and RR fluxes. The simplest examples have descriptions as cosets, generalizing the three-dimensional nilmanifold. They can also be thought of as twisted tori. We derive a formula for the (super)potential governing the light fields, which is generated by the fluxes and certain "twists" in the geometry. Detailed consideration of an example also gives strong evidence that in some cases, these exotic geometries are related by smooth transitions to standard Calabi-Yau or G 2 compactifications of M-theory.

T-fold" backgrounds are generically-nongeometric compactifications of string theory, described by T n fibrations over a base N with transition functions in the perturbative T-duality group. We review Hull's doubled torus formalism, which geometrizes these backgrounds, and use the formalism to constrain the D-brane spectrum (to leading order in g s and α ′ ) on T n fibrations over S 1 with O(n, n; Z) monodromy. We also discuss the (approximate) moduli space of such branes and argue that it is always geometric. For a D-brane located at a point on the base N , the classical "D-geometry" is a T n fibration over a multiple cover of N .