Type I on (Generalized) Voisin-Borcea Orbifolds and Non-perturbative Orientifolds

We consider non-perturbative four dimensional N=1 space-time supersymmetric orientifolds corresponding to Type I compactifications on (generalized) Voisin-Borcea orbifolds. Some states in such compactifications arise in ``twisted'' open string sectors which lack world-sheet description in terms of D-branes. Using Type I-heterotic duality as well as the map between Type IIB orientifolds and F-theory we are able to obtain the massless spectra of such orientifolds. The four dimensional compactifications we discuss in this context are examples of chiral N=1 supersymmetric string vacua which are non-perturbative from both orientifold and heterotic points of view. In particular, they contain both D9- and D5-branes as well as non-perturbative ``twisted'' open string sector states. We also explain the origins of various inconsistencies arising in such compactifications for certain choices of the gauge bundle.Comment: 34 pages, revtex; minor misprints correcte

Geometry of Orientifolds with NS-NS B-flux

We discuss geometry underlying orientifolds with non-trivial NS-NS B-flux. If D-branes wrap a torus with B-flux the rank of the gauge group is reduced due to non-commuting Wilson lines whose presence is implied by the B-flux. In the case of D-branes transverse to a torus with B-flux the rank reduction is due to a smaller number of D-branes required by tadpole cancellation conditions in the presence of B-flux as some of the orientifold planes now have the opposite orientifold projection. We point out that T-duality in the presence of B-flux is more subtle than in the case with trivial B-flux, and it is precisely consistent with the qualitative difference between the aforementioned two setups. In the case where both types of branes are present, the states in the mixed (e.g., 59) open string sectors come with a non-trivial multiplicity, which we relate to a discrete gauge symmetry due to non-zero B-flux, and construct vertex operators for the the mixed sector states. Using these results we revisit K3 orientifolds with B-flux (where K3 is a T^4/Z_M orbifold) and point out various subtleties arising in some of these models. For instance, in the Z_2 case the conformal field theory orbifold does not appear to be the consistent background for the corresponding orientifolds with B-flux. This is related to the fact that non-zero B-flux requires the presence of both O5^- as well as O5^+ planes at various Z_2 orbifold fixed points, which appears to be inconsistent with the presence of the twisted B-flux in the conformal field theory orbifold. We also consider four dimensional N=2 and N=1 supersymmetric orientifolds. We construct consistent four dimensional models with B-flux which do not suffer from difficulties encountered in the K3 cases.Comment: 79 pages, revte

Toward Solving the Cosmological Constant Problem?

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions. In particular, by adding higher curvature terms in the bulk action we are able to find smooth solutions with the property that the 4-dimensional part of the brane world-volume is flat for a range of positive values of the brane tension.Comment: 45 pages, revtex, 8 eps figure

Diluting solutions of the cosmological constant problem

We discuss the cosmological constant problem in the context of higher codimension brane world scenarios with infinite-volume extra dimensions.Comment: 11 pages, Revtex, reference adde

On Gauge Dynamics and SUSY Breaking in Orientiworld

In the Orientiworld framework the Standard Model fields are localized on D3-branes sitting on top of an orientifold 3-plane. The transverse 6-dimensional space is a non-compact orbifold (or a more general conifold). The 4-dimensional gravity on D3-branes is reproduced due to the 4-dimensional Einstein-Hilbert term induced at the quantum level. The orientifold 3-plane plays a crucial role, in particular, without it the D3-brane world-volume theories would be conformal due to the tadpole cancellation. We study non-perturbative gauge dynamics in various N=1 supersymmetric orientiworld models based on the Z_3 as well as Z_5 and Z_7 orbifold groups. Our discussions illustrate that there is a rich variety of supersymmetry preserving dynamics in some of these models. On the other hand, we also find some models with dynamical supersymmetry breaking.Comment: 21 pages, revtex, minor misprints corrected (to appear in Int. J. Mod. Phys. A

A Review of Three-Family Grand Unified String Models

We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid analysis of their phenomenological properties. We compute tree-level superpotentials for these models. These superpotentials are used to analyze the issues of proton stability (doublet-triplet splitting and R-parity violating terms) and Yukawa mass matrices. To have agreement with phenomenological data all these models seem to require certain degree of fine-tuning. We also analyze the possible patterns of supersymmetry breaking in these models. We find that the supersymmetry breaking scale comes out either too high to explain the electroweak hierarchy problem, or below the electroweak scale unless some degree of fine-tuning is involved. Thus, none of the models at hand seem to be phenomenologically flawless.Comment: 49 pages, Revtex 3.0; one ps figure included. To appear in the Review section of Int.J.Mod.Phy

Anomaly Free Non-Supersymmetric Large NN Gauge Theories from Orientifolds

We construct anomaly free non-supersymmetric large N gauge theories from orientifolds of Type IIB on C^3/G orbifolds. In particular, massless as well as tachyonic one-loop tadpoles are cancelled in these models. This is achieved by starting with ${\cal N}=1,2$ supersymmetric orientifolds with well defined world-sheet description and including discrete torsion (which breaks supersymmetry) in the orbifold action. In this way we obtain non-trivial non-chiral as well as anomaly free chiral large N gauge theories. We point out certain subtleties arising in the chiral cases. Subject to certain assumptions, these theories are shown to have the property that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ oriented theory. This generalizes the analogous results recently obtained in supersymmetric large N gauge theories from orientifolds, as well as in (non)supersymmetric large N gauge theories without orientifold planes.Comment: 18 pages, revtex, minor misprints corrected, a clarifying footnote added (to appear in Phys. Rev. D

D=4, N=1, Type IIA Orientifolds

We study D=4, N=1, type IIA orientifold with orbifold group $Z_N$ and $Z_N \times Z_M$. We calculate one-loop vacuum amplitudes for Klein bottle, cylinder and Mobius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the $Z_4$, $Z_8$, $Z'_8$, $Z'_{12}$ orientifolds while there is no solution for $Z_3$, $Z_7$, $Z_6$, $Z'_6$, $Z_{12}$. The $Z_4 \times Z_4$ type IIA orientifold is also constructed by introducing four different configurations of 6-branes. We argue about perturbative versus non-perturbative orientifold vacua under T- duality between the type IIA and the type IIB $Z_N$ orientifolds in four dimensions.Comment: 32 pages, LaTe