Orientifold Singularities Research Articles

Aether, dark energy and string compactifications.

The nineteenth-century aether died with special relativity but was resurrected by general relativity in the form of dark energy; a tensile material with tension equal to its energy density. Such a material is provided by the D-branes of string-theory; these can support the fields of supersymmetric particle-physics, although their energy density is cancelled by orientifold singularities upon compactification. Dark energy can still arise from supersymmetry-breaking anti-D-branes but it is probably time-dependent. Recent results on time-dependent compactifications to an FLRW universe with late-time accelerated expansion are reviewed.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

On supersymmetry breaking vacua from D-branes at orientifold singularities

We present a large class of models of D-branes at (orientifold) Calabi-Yau sin- gularities which enjoy dynamical supersymmetry breaking at low energy, by means of either the SU(5) or 3–2 supersymmetry breaking models. Once embedded in a warped throat or, equivalently, in a large N theory, all models display an instability along a Coulomb branch direction towards supersymmetry preserving vacua. Interestingly, the nature of the run- away mechanism is model-independent and has a precise geometrical interpretation. This naturally suggests the properties a Calabi-Yau singularity should have in order for such instability not to occur.

Orientifolds and duality cascades: confinement before the wall

We consider D-branes at orientifold singularities and discuss two properties of the corresponding low energy four-dimensional effective theories which are not shared, generically, by other Calabi-Yau singularities. The first property is that duality cascades are finite and, unlike ordinary ones, do not require an infinite number of degrees of freedom to be UV-completed. The second is that orientifolds tend to stabilize runaway directions. These two properties can have interesting implications and widen in an intriguing way the variety of gauge theories one can describe using D-branes.

D-brane instantons as gauge instantons in orientifolds of chiral quiver theories

Systems of D3-branes at orientifold singularities can receive non-perturbative D-brane instanton corrections, inducing field theory operators in the 4d effective theory. In certain non-chiral examples, these systems have been realized as the infrared endpoint of a Seiberg duality cascade, in which the D-brane instanton effects arise from strong gauge theory dynamics. We present the first UV duality cascade completion of chiral D3-brane theories, in which the D-brane instantons arise from gauge theory dynamics. Chiral examples are interesting because the instanton fermion zero mode sector is topologically protected, and therefore lead to more robust setups. As an application of our results, we provide a UV completion of certain D-brane orientifold systems recently claimed to produce conformal field theories with conformal invariance broken only by D-brane instantons.

NOTES ON UNORIENTED D-BRANE INSTANTONS

We review basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons, which is our main focus here, and threshold corrections to BPS-saturated couplings. We then consider nonperturbative superpotentials generated by "gauge" and "exotic" instantons living on D3-branes at orientifold singularities. Moreover, we discuss the interplay between worldsheet and D-string instantons on T4/Z2. We focus on a 4-Fermi amplitude, give Heterotic and perturbative Type I descriptions, and offer a multi-D-string instanton interpretation. We conclude with possible interesting developments.

Gauge threshold corrections for local orientifolds

We study gauge threshold corrections for systems of fractional branes at local orientifold singularities and compare with the general Kaplunovsky-Louis expression for locally supersymmetric = 1 gauge theories. We focus on branes at orientifolds of the 3/4, 3/6 and 3/6' singularities. We provide a CFT construction of these theories and compute the threshold corrections. Gauge coupling running undergoes two phases: one phase running from the bulk winding scale to the string scale, and a second phase running from the string scale to the infrared. The first phase is associated to the contribution of = 2 sectors to the IR β functions and the second phase to the contribution of both = 1 and = 2 sectors. In contrast, naive application of the Kaplunovsky-Louis formula gives single running from the bulk winding mode scale. The discrepancy is resolved through 1-loop non-universality of the holomorphic gauge couplings at the singularity, induced by a 1-loop redefinition of the twisted blow-up moduli which couple differently to different gauge nodes. We also study the physics of anomalous and non-anomalous U(1)s and give a CFT description of how masses for non-anomalous U(1)s depend on the global properties of cycles.

Anomalous U(1)'s in Type I and Type IIB D = 4, N = 1 string vacua

We study the cancellation of U(1) anomalies in Type I and Type IIB D = 4, N = 1 string vacua. We first consider the case of compact toroidal Z N Type IIB orientifolds and then proceed to the non-compact case of Type IIB D3-branes at orbifold and orientifold singularities. Unlike the case of the heterotic string we find that for each given vacuum one has generically more than one U(1) with non-vanishing triangle anomalies. There is a generalized Green-Schwarz mechanism by which these anomalies are cancelled. This involves only the Ramond-Ramond scalars coming from the twisted closed string spectrum but not those coming from the untwisted sector. Associated to the anomalous U(1)'s there are field-dependent Fayet-Iliopoulos terms whose mass scale is fixed by undetermined vev's of the NS-NS partners of the relevant twisted RR fields. Thus, unlike what happens in heterotic vacua, the masses of the anomalous U(1)'s gauge bosons may be arbitrarily light. In the case of D3-branes at singularities, appropriate factorization of the U(1)'s constrains the Chan-Paton matrices beyond the restrictions from cancellation of non-abelian anomalies. These conditions can be translated to constraints on the T-dual Type IIB brane box configurations. We also construct a new large family of N = 1 chiral gauge field theories from D3-branes at orientifold singularities, and check its non-abelian and U(1) anomalies cancel.

A note on superconformal N = 2 theories and orientifolds

We construct the T-duals of certain type IIA brane configurations with one compact dimension (elliptic models) which contain orientifold planes. These configurations realize four-dimensional N = 2 finite field theories. For elliptic models with two negatively charged orientifold six-planes, the T-duals are given by D3-branes at singularities in the presence of O7-planes and D7-branes. For elliptic models with two oppositely charged orientifold planes, the T-duals are D3-branes at a different kind of orientifold singularities, which do not require D7-branes. We construct the adequate orientifold groups, and show that the cancellation of twisted tadpoles is equivalent to the finiteness of the corresponding field theory. One family of models contains orthogonal and symplectic gauge factors at the same time. These new orientifolds can also be used to define some six-dimensional RG fixed points which have been discussed from the type IIA brane configuration perspective.