Orientifold Compactifications Research Articles

On D-brane dynamics and moduli stabilization

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of [Formula: see text] orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in [Formula: see text] orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of “brane supersymmetry breaking” and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kähler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kähler moduli stabilization, this is not always the case.

Shift-symmetries and gauge coupling functions in orientifolds and F-theory

We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional super-gravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional mathcal{N} = 1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.

The Euler characteristic correction to the K\xe4hler potential \u2014 revisited

We confirm the leading α′3 correction to the 4d, mathcal{N}=1 Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the α′3-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an SU(3) structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multiplied by a non-trivial Weyl factor. Performing a Kaluza-Klein reduction on the modified background we derive the α′3-corrected kinetic terms for the dilaton and the Kähler deformations of the internal Calabi-Yau threefold for arbitrary h1,1. We analyze these kinetic terms in the 4d, mathcal{N}=2 un-orientifolded theory, confirming the expected correction to the Kähler moduli space pre-potential, as well as in the 4d, mathcal{N}=1 orientifolded theory, thus determining the corrections to the Kähler potential and Kähler coordinates.

Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization

In the context of non-geometric type II orientifold compactifications, there have been two formulations for representing the various NS-NS Bianchi-identities. In the first formulation, the standard three-form flux ($H_3$), the geometric flux ($\omega$) and the non-geometric fluxes ($Q$ and $R$) are expressed by using the real six-dimensional indices (e.g. $H_{ijk}, \omega_{ij}{}^k, Q_i{}^{jk}$ and $R^{ijk}$), and this formulation has been heavily utilized for simplifying the scalar potentials in toroidal-orientifolds. On the other hand, relevant for the studies beyond toroidal backgrounds, a second formulation is utilized in which all flux components are written in terms of various involutively even/odd $(2,1)$- and $(1,1)$-cohomologies of the complex threefold. In the lights of recent model building interests and some observations made in arXiv:0705.3410 and arXiv:0709.2186, in this article, we revisit two most commonly studied toroidal examples in detail to illustrate that the present forms of these two formulations are not completely equivalent. To demonstrate the same, we translate all the identities of the first formulation into cohomology ingredients, and after a tedious reshuffling of the subsequent constraints, interestingly we find that all the identities of the second formulation are embedded into the first formulation which has some additional constraints. In addition, we look for the possible solutions of these Bianchi identities in a detailed analysis, and we find that some solutions can reduce the size of scalar potential very significantly, and in some cases are too strong to break the no-scale structure completely. Finally, we also comment on the influence of imposing some of the solutions of Bianchi identities in studying moduli stabilization.

Type IIB on S 3 × S 3 through Q & P fluxes

We study a class of orientifold compactifications of type IIB supergravity with fluxes down to 4D in connection with truncations of half-maximal gauged supergravities yielding isotropic STU-models with minimal supersymmetry. In this context, we make use of a group-theoretical approach in order to derive flux-induced superpotentials for different IIB backgrounds. We first review the toroidal case yielding GKP-like superpotentials characterised by their \emph{no-scale} behaviour. We then turn to $S^{3} \times S^{3}$ and $S^{3} \times \mathbb{T}^{3}$, which, surprisingly, give rise to effective descriptions of non-geometric $Q$- and $P$-fluxes through globally geometric non-toroidal compactifications. As a consequence, such constructions break the no-scale symmetry without invoking any non-perturbative effects.

Domain walls inside localised orientifolds

The equations of motion of toroidal orientifold compactifications with fluxes are in one-to-one correspondence with gauged supergravity if the orientifold (and D-brane) sources are smeared over the compact space. This smeared limit is identical to the approximation that ignores warping. It is therefore relevant to compare quantities obtained from the gauged supergravity with the true 10d solution with localised sources. In this paper we find the correspondence between BPS domain walls in gauged SUGRA and 10D SUGRA with localised sources. Our model is the simplest orientifold with fluxes we are aware of: an O6/D6 compactification on T^3/Z_2 in massive IIA with H_3-flux. The BPS domain walls correspond to a O6/D6/NS5/D8 bound state. Our analysis reveals that the domain wall energy computed in gauged SUGRA is unaffected by the localisation of the O6/D6 sources.

On modular completion of generalized flux orbits

In the context of type IIB orientifold compactification with the presence of (non-)geometric fluxes, we conjecture a modular completed version of the generalized flux-orbits of various NS-NS and RR fluxes. Subsequently, considering two explicit examples with frozen complex structure moduli, we illustrate the utility of these new flux orbits in a very compact rearrangement of the four dimensional effective scalar potential.

Effective upliftings in Large volume compactifications

After reviewing several mechanisms proposed to get a dS/Minkowski vacuum in moduli stabilization scenarios of type-IIB superstring orientifold compactifications we propose a criterium for characterizing those that may effectively lead to a positive small cosmological constant. We suggest that the variation in the expectation value of a good uplifting term, due to the shift in the minimum of the potential after uplifting, is much smaller than the original cosmological constant. This is studied with some detail in Large volume scenarios where the dependency on the volume direction is rather generic and easy to spot. Here we find that an uplifting term in the potential, with generic form Vup∼1/Vγ, should be restricted to the one satisfying γ≪12. Such a bound might explain why in models previously studied no uplifting has been achieved, and gives motivations to study a novel proposal of dilaton dependent uplifting mechanism for which no numerical studies has been performed before. We find that in this case it is actually possible to get a dS vacuum, but still leave open the question of a more precise discrimination feature the good uplifting mechanisms should satisfy.

Helical phase inflation via non-geometric flux compactifications: from natural to starobinsky-like inflation

We show that a new class of helical phase inflation models can be simply realized in minimal supergravity, wherein the inflaton is the phase component of a complex field and its potential admits a deformed helicoid structure. We find a new unique complex-valued index χ that characterizes almost the entire region of the n s − r plane favored by new Planck observations. Continuously varying the index χ, predictions interpolate from quadratic/natural inflation parameterized by a phase/axion decay constant to Starobinsky-like inflation parameterized by the α-parameter. We demonstrate that the simple supergravity construction realizing Starobinsky-like inflation can be obtained from a more microscopic model by integrating out heavy fields, and that the flat phase direction for slow-roll inflation is protected by a mildly broken global U(1) symmetry. We study the geometrical origin of the index χ, and find that it corresponds to a linear constraint relating Kahler moduli. We argue that such a linear constraint is a natural result of moduli stabilization in Type II orientifold compactifications on Calabi-Yau threefolds with geometric and non-geometric fluxes. Possible choices for the index χ are discrete points on the complex plane that relate to the distribution of supersymmetric Minkowski vacua on moduli space. More precise observations of the inflationary epoch in the future may provide a better estimation of the index χ. Since χ is determined by the fluxes and vacuum expectation values of complex structure moduli, such observations would characterize the geometry of the internal space as well.

Discrete symmetries from hidden sectors

We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination of U(1) gauge factors of the visible as well as the hidden sector. This more general ansatz significantly increases the probability of finding a discrete symmetry in the low energy effective action. Applied to globally consistent MSSM-like Gepner constructions we find multiple models that allow for matter parity or Baryon triality.

How well can we really determine the scale of inflation?

A detection of primordial B-modes has been heralded not only as a smoking gun for the existence of inflation, but also as a way to establish the scale at which inflation took place. In this paper we critically reinvestigate the connection between a detection of primordial gravity waves and the scale of inflation. We consider whether the presence of additional fields and non-adiabaticity during inflation may have provided an additional source of primordial B-modes competitive with those of the quasi-de Sitter vacuum. In particular, we examine whether the additional sources could provide the dominant signal, which could lead to a misinterpretation of the scale of inflation. In light of constraints on the level of non-Gaussianity coming from Planck we find that only hidden sectors with strictly gravitationally strength couplings provide a feasible mechanism. The required model building is somewhat elaborate, and so we discuss possible UV completions in the context of Type IIB orientifold compactifications with RR axions. We find that an embedding is possible and that dangerous sinusoidal corrections can be suppressed through the compactification geometry. Our main result is that even when additional sources of primordial gravity waves are competitive with the inflaton, a positive B-mode detection would still be a relatively good indicator of the scale of inflation. This conclusion will be strengthened by future constraints on both non-Gaussianity and CMB polarization.

Flux-induced soft terms on type IIB/F-theory matter curves and hypercharge dependent scalar masses

Closed string fluxes induce generically SUSY-breaking soft terms on supersymmetric type IIB orientifold compactifications with D3/D7 branes. This was studied in the past by inserting those fluxes on the DBI+CS actions for adjoint D3/D7 fields, where D7-branes had no magnetic fluxes. In the present work we generalise those computations to the phenomenologically more relevant case of chiral bi-fundamental fields laying at 7-brane intersections and F-theory local matter curves. We also include the effect of 7-brane magnetic flux as well as more general closed string backgrounds, including the effect of distant (anti-)D3-branes. We discuss several applications of our results. We find that squark/slepton masses become in general flux-dependent in F-theory GUT's. Hypercharge-dependent non-universal scalar masses with a characteristic sfermion hierarchy m_E^2 < m_L^2 < m_Q^2 < m_D^2 < m_U^2 are obtained. There are also flavor-violating soft terms both for matter fields living at intersecting 7-branes or on D3-branes at singularities. They point at a very heavy sfermion spectrum to avoid FCNC constraints. We also discuss the possible microscopic description of the fine-tuning of the EW Higgs boson in compactifications with a MSSM spectrum.

BPS domain walls from backreacted orientifolds

Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold compactification in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We find and discuss the BPS domain walls both when the O6 planes are smeared and localised. When the O6 planes are localised the domain wall solutions live in a warped compactification. In order to get explicit expressions we also consider the non-compact versions of the solutions for which the O6 planes have been traded for D6 branes. Through T-duality we obtain partially localised solutions for compactifications to four dimensions using O3 planes with 3-form fluxes.

On [formula omitted] corrections in [formula omitted] F-theory compactifications

We consider N=1 F-theory and Type IIB orientifold compactifications and derive new α′ corrections to the four-dimensional effective action. They originate from higher derivative corrections to eleven-dimensional supergravity and survive the M-theory to F-theory limit. We find a correction to the Kähler potential depending on the volume of a non-trivial intersection curve of seven-branes. At weak string coupling this correction arises from the intersection of D7-branes with the O7-plane. We also analyze a four-dimensional higher curvature correction.

Four Kähler moduli stabilisation in type IIB orientifolds with K3-fibred Calabi-Yau threefold compactification

We present a concrete and consistent procedure to generate one kind of non-perturbative superpotential, including the gaugino condensation corrections and poly-instanton corrections, in type IIB orientifold compactification with four Kahler Moduli. Then we use this kind of superpotential as well as the alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli on a general Calabi-Yau manifold with typical K3-fibred volume form. In our construction, the considered Calabi-Yau threefolds are K3-fibred and admit at least one del Pezzo surface and one W-surface. Searching through all existing four dimensional reflexive lattice polytopes, we find 23 of them fulfilling all the requirements.

Stringy hidden valleys

We study gauge theories where quasi-hidden sectors are added to the MSSM for the sake of string consistency conditions which would otherwise not be satisfied. We focus on quiver gauge theories motivated by weakly coupled type II orientifold compactifications. Model independent features in this class include an anomalous U(1)_V symmetry which protects messenger masses and has strong consequences for superpotential couplings, a rich phenomenology of heavy and light Z' bosons, and axionic couplings required for anomaly cancellation via the Green-Schwarz mechanism. We discuss possibilities for dark matter and supersymmetry breaking in light of these generic features. Dark matter is necessarily non-baryonic, though many dark matter candidates have weak interactions. Most models have a U(1)_V Y Y anomaly whose cancellation requires couplings which allow for dark matter annihilation into photons through intermediate axions or anomalous Z' bosons, as in two recently proposed scenarios. There is often an additional non-anomalous U(1) symmetry which can give rise to a Fayet-like model of metastable supersymmetry breaking. Breaking of supersymmetry via SQCD can also be realized and flavor masses are often protected. Natural possibilities for mediation include gauge mediation, Z' mediation, and D-instanton mediation, though it is not possible to realize minimal gauge mediation with messengers added for string consistency.

D-brane instantons on non-Spin cycles

Abstract We show that non-Spin cycles in type IIB Calabi-Yau orientifold compactifications with vanishing B field naturally support orientifold-invariant D-brane instantons. These instantons, associated to the holomorphic cotangent bundle of the non-Spin cycle, can lead to non-perturbative corrections to the superpotential.

Fractional branes, warped compactifications and backreacted orientifold planes

Abstract The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the worldvolume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional scalars that flow along the massless directions in the no-scale potential. Depending on the details of the fluxes these flows can be supersymmetric domain wall flows. Our solutions provide explicit examples of backreacted orientifold planes in compactifications with non-constant moduli.

Global embeddings for branes at toric singularities

Abstract We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP 0)3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

The type IIB string axiverse and its low-energy phenomenology

Abstract We study closed string axions in type IIB orientifold compactifications. We show that for natural values of the background fluxes the moduli stabilisation mechanism of the LARGE Volume Scenario (LVS) gives rise to an axiverse characterised by the presence of a QCD axion plus many light axion-like particles whose masses are logarithmically hierarchical. We study the phenomenological features of the LVS axiverse, deriving the masses of the axions and their couplings to matter and gauge fields. We also determine when closed string axions can solve the strong CP problem, and analyse the first explicit examples of semi-realistic models with stable moduli and a QCD axion candidate which is not eaten by an anomalous Abelian gauge boson. We discuss the impact of the choice of inflationary scenario on the LVS axiverse, and summarise the astrophysical, cosmological and experimental constraints upon it. Moreover, we show how models can be constructed with additional light axion-like particles that could explain some intriguing astrophysical anomalies, and could be searched for in the next generation of axion helioscopes and light-shining-through-a-wall experiments.