Orbifold Compactifications Research Articles

Phenomenological aspects of heterotic orbifold models at one loop

We provide a detailed study of the phenomenology of orbifold compactifications of the heterotic string within the context of supergravity effective theories. Our investigation focuses on those models where the soft Lagrangian is dominated by loop contributions to the various soft supersymmetry breaking parameters. Such models typically predict non-universal soft masses and are thus significantly different from minimal supergravity and other universal models. We consider the pattern of masses that are governed by these soft terms and investigate the implications of certain indirect constraints on supersymmetric models, such as flavor-changing neutral currents, the anomalous magnetic moment of the muon and the density of thermal relic neutralinos. We also comment on the possible discovery of these models at the LHC. These string-motivated models show a novel behavior that interpolates between the phenomenology of unified supergravity models and models dominated by the superconformal anomaly.

Gaugino condensates and fluxes in [formula omitted] effective superpotentials

In the framework of orbifold compactifications of heterotic and type II orientifolds, we study effective N = 1 supergravity potentials arising from fluxes and gaugino condensates. These string solutions display a broad phenomenology which we analyze using the method of N = 4 supergravity gaugings. We give examples in type II and heterotic compactifications of combined fluxes and condensates leading to vacua with naturally small supersymmetry breaking scale controlled by the condensate, cases where the supersymmetry breaking scale is specified by the fluxes even in the presence of a condensate and also examples where fluxes and condensates conspire to preserve supersymmetry.

Exploring the SO(32) heterotic string

We give a complete classification of Z_N orbifold compactification of the heterotic SO(32) string theory and show its potential for realistic model building. The appearance of spinor representations of SO(2n) groups is analyzed in detail. We conclude that the heterotic SO(32) string constitutes an interesting part of the string landscape both in view of model constructions and the question of heterotic-type I duality.

HIGHER DERIVATIVE OPERATORS AS COUNTERTERMS IN ORBIFOLD COMPACTIFICATIONS

In the context of 5D N = 1 supersymmetric models compactified on S1/Z2 or S1/(Z2×Z2′) orbifolds and with brane-localized superpotential, higher derivative operators are generated radiatively as one-loop counterterms to the mass of the (brane or zero mode of the bulk) scalar field. It is shown that the presence of such operators which are brane-localised is not related to the mechanism of supersymmetry breaking considered (F-term, discrete or continuous Scherk–Schwarz breaking) and initial supersymmetry does not protect against the dynamical generation of such operators. Since in many realistic models the scalar field is commonly regarded as the Higgs field, and the higher derivative operators seem a generic presence in orbifold compactifications, we stress the importance of these operators for solving the hierarchy problem.

Higher derivative operators from Scherk-Schwarz supersymmetry breaking on Script T2/Z2.

In orbifold compactifications on T^2/Z_2 with Scherk-Schwarz supersymmetry breaking, it is shown that (brane-localised) superpotential interactions and (bulk) gauge interactions generate at one-loop higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field. These brane-localised operators are generated by integrating out the bulk modes of the initial theory which, although supersymmetric, is nevertheless non-renormalisable. It is argued that such operators, of non-perturbative origin and not protected by non-renormalisation theorems, are generic in orbifold compactifications and play a crucial role in the UV behaviour of the two-point Green function of the scalar field self-energy. Their presence in the action with unknown coefficients prevents one from making predictions about physics at (momentum) scales close to/above the compactification scale(s). Our results extend to the case of two dimensional orbifolds, previous findings for S^1/Z_2 and S^1/(Z_2 x Z_2') compactifications where brane-localised higher derivative operators are also dynamically generated at loop level, regardless of the details of the supersymmetry breaking mechanism. We stress the importance of these operators for the hierarchy and the cosmological constant problems in compactified theories.

Remarks on flavour mixings from orbifold compactification

We consider five-dimensional SU(5) GUT models based on the orbifold S1/(Z2 × Z′2), and study the different possibilities of placing the SU(5) matter multiplets in three possible locations, namely, the two branes at the two orbifold fixed points and SU(5) bulk. We demonstrate that if flavour hierarchies originate solely from geometrical suppressions due to wave function normalization of fields propagating in the bulk, then it is not possible to satisfy even the gross qualitative behaviour of the CKM and MNS matrices regardless of where we place the matter multiplets.

Higher derivative operators from transmission of supersymmetry breaking onS1/Z2

We discuss the role that higher derivative operators play in field theory orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz) breaking of supersymmetry. Integrating out the bulk fields generates brane-localised higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field, identified with the Higgs field in many realistic models. Both Yukawa and gauge interactions are considered and the one-loop results found can be used to study the ``running'' of the scalar field mass with respect to the momentum scale in 5D orbifolds. In particular this allows the study of the behaviour of the mass under UV scaling of the momentum. The relation between supersymmetry breaking and the presence of higher derivative counterterms to the mass of the scalar field is investigated. This shows that, regardless of the breaking mechanism, (initial) supersymmetry cannot, in general, prevent the emergence of such operators. Some implications for phenomenology of the higher derivative operators are also presented.

On orbifold compactification of Script N = 2 supergravity in five dimensions

We study compactification of five dimensional ungauged N=2 supergravity coupled to vector- and hypermultiplets on orbifold $S^1/Z_2$. In the model the vector multiplets scalar manifold is arbitrary while the hypermultiplet scalars span a generalized self dual Einstein manifold constructed by Calderbank and Pedersen. The bosonic and the fermionic sector of the low energy effective N=1 supergravity in four dimensions are derived.

Heterotic brane world

Orbifold compactification of heterotic E{sub 8}xE{sub 8}{sup '} string theory is a source for promising grand unified model building. It can accommodate the successful aspects of grand unification while avoiding problems like doublet-triplet splitting in the Higgs sector. Many of the phenomenological properties of the four-dimensional effective theory find an explanation through the geometry of compact space and the location of matter and Higgs fields. These geometrical properties can be used as a guideline for realistic model building.

Model ofCPviolation from an extra dimension

We construct a realistic model of CP violation in which CP is broken in the process of dimensional reduction and orbifold compactification from a five dimensional theories with $SU(3)\times SU(3) \times SU(3)$ gauge symmetry. CP violation is a result of the Hosotani type gauge configuration in the higher dimension.

Higgs-gauge unification without tadpoles

In orbifold gauge theories localized tadpoles can be radiatively generated at the fixed points where U ( 1 ) subgroups are conserved. If the Standard Model Higgs fields are identified with internal components of the bulk gauge fields (Higgs-gauge unification) in the presence of these tadpoles the Higgs mass becomes sensitive to the UV cutoff and electroweak symmetry breaking is spoiled. We find the general conditions, based on symmetry arguments, for the absence/presence of localized tadpoles in models with an arbitrary number of dimensions D. We show that in the class of orbifold compactifications based on T D − 4 / Z N ( D even, N > 2 ) tadpoles are always allowed, while on T D − 4 / Z 2 (arbitrary D) with fermions in arbitrary representations of the bulk gauge group tadpoles can only appear in D = 6 dimensions. We explicitly check this with one- and two-loops calculations.

Modular invariant gaugino condensation in the presence of an anomalous [formula omitted

Starting from the previously constructed effective supergravity theory below the scale of U ( 1 ) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Questions we address include vacuum stability and the masses of the various moduli fields, including those associated with flat directions at the U ( 1 ) breaking scale, and of their fermionic superpartners. The issue of soft supersymmetry-breaking masses in the observable sector presents a particularly serious challenge for this class of models.

Inflation in string-inspired cosmology and suppression of CMB low multipoles

We construct a string-inspired nonsingular cosmological scenario in which an inflaton field is driven up the potential before the graceful exit by employing a low-energy string effective action with an orbifold compactification. This sets up an initial condition for the inflaton to lead to a sufficient number of e-foldings and to generate a nearly scale-invariant primordial density perturbation during slow-roll inflation. Our scenario provides an interesting possibility to explain a suppressed power spectrum at low multipoles due to the presence of the modulus-driven phase prior to slow-roll inflation and thus can leave a strong imprint of extra dimensions in observed CMB anisotropies.

Regularization techniques for the radiative corrections of Wilson lines and Kaluza-Klein states

Within an effective field theory framework we compute the most general structure of the one-loop corrections to the 4D gauge couplings in one- and two-dimensional orbifold compactifications with nonvanishing constant gauge background (Wilson lines). Although such models are nonrenormalizable, we keep the analysis general by considering the one-loop corrections in three regularization schemes: dimensional regularization (DR), zeta-function regularization (ZR), and proper-time cutoff regularization (PT). The relations among the results obtained in these schemes are carefully addressed. With minimal redefinitions of the parameters involved, the results obtained for the radiative corrections can be applied to most orbifold compactifications with one or two compact dimensions. The link with string theory is discussed. We mention a possible implication for the gauge coupling unification in such models.

Topological masses from broken supersymmetry

We develop a formalism for computing one-loop gravitational corrections to the effective action of D-branes. In particular, we study bulk to brane mediation of supersymmetry breaking in models where supersymmetry is broken at the tree-level in the closed string sector (bulk) by Scherk–Schwarz boundary conditions, while it is realized on a collection of D-branes in a linear or non-linear way. We compute the gravitational corrections to the fermion masses m 1/2 (gauginos or goldstino) induced from the exchange of closed strings, which are non-vanishing for world-sheets with Euler characteristic −1 (“genus 3/2”) due to a string diagram with one handle and one hole. We show that the corrections have a topological origin and that in general, for a small gravitino mass, the induced mass behaves as m 1/2∝ g 4 m 3/2, with g the gauge coupling. In generic orbifold compactifications however, this leading term vanishes as a consequence of cancellations caused by discrete symmetries, and the remainder is exponentially suppressed by a factor of exp(−1/ α′ m 2 3/2).

Trinification with sin2θW=3/8 and see-saw neutrino mass

We realize a supersymmetric trinification model with three families of (27tri+27tri+27tri) by the Z3 orbifold compactification with two Wilson lines. It is possible to break the trinification group to the supersymmetric standard model. This model has several interesting features: the hypercharge quantization, sin2θW0=3/8, naturally light neutrino masses, and introduction of R-parity. The hypercharge quantization is realized by the choice of the vacuum, naturally leading toward a supersymmetric standard model.

Model building with gauge-Yukawa unification

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge-Yukawa coupling unification, g_i=y_f, in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactification. We consider gauge-Yukawa unified models based on a variety of four dimensional symmetries, including SO(10), SU(5), Pati-Salam symmetry, trinification, and the Standard Model. Only in the case of Pati-Salam and the Standard Model symmetry, we do obtain gauge-Yukawa unification. Partial gauge-Yukawa unification is also briefly discussed.

Two-loop superstrings on orbifold compactifications

The two-loop chiral measure for superstring theories compactified on Z 2 reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure in the twisted sectors and the identification of a subtle worldsheet supersymmetric and supermoduli dependent shift in the Prym period. The construction is generalized to compactifications which involve more general NS backgrounds preserving worldsheet supersymmetry. The measures are unambiguous and independent of the gauge slice. Two applications are presented, both to superstring compactifications where 4 dimensions are Z 2 -twisted and where the GSO projection involves a chiral summation over spin structures. The first is an orbifold by a single Z 2 -twist; here, orbifolding reproduces a supersymmetric theory and it is shown that its cosmological constant indeed vanishes. The second model is of the type proposed by Kachru–Kumar–Silverstein and additionally imposes a Z 2 -twist by the parity of worldsheet fermion number; it is shown here that the corresponding cosmological constant does not vanish pointwise on moduli space.

Kasner and mixmaster behavior in universes with equation of statew>~1

We consider cosmological models with a scalar field with equation of state $w>~1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1.$ We generalize the results to theories where the scalar field couples to p forms and show that there exists a finite value of w, depending on the p-forms, such that chaotic oscillations are suppressed. We show that ${Z}_{2}$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.

N = 1 and nonsupersymmetric open string theories in six and four space-time dimensions

This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they show up in electro-magnetic fields. We quantize the zero-modes for toroidal compactifications, too. As an application we calculate the commutator of the coordinate fields in the case of general constant Neveu-Schwarz U(1)-field strengths. Thereby we confirm previous results on non-commutativity of open string theories in Neveu-Schwarz backgrounds. Chapter 5 reviews the results of a former publication [1] on asymmetric orientifolds, supplemented by some recent insights in connection with chapter 4. Chapter 6 summarizes publication [2] where we investigated to what extend one can build phenomenologically interesting models from toroidal orientifolds. By turning on magnetic fluxes on D9-branes we induce chiral fermions. Most calculations are performed in an (equivalent) T-dual picture. Here the number of chiral fermions is given by the topological intersection number of D-branes. In orientifolds of toroidal compactifications one obtains either non-chiral or non-supersymmetric orientifold solutions. However both properties can be reconciled in orientifolds that are obtained from specific supersymmetric orbifold compactifications. In chapter 7 we present the ``sigma Omega'' -Orientifold on a T^6/Z(4) orbifold. As a very attractive example we investigate a supersymmetric U(4) x U(2)^3_L x U(2)^3_R model that is broken to an MSSM-like model by switching on suitable background fields in the LEEA. This chapter is based on our publication [3]. An appendix is supplemented with formulas applied in the text, as well as proofs to two theorems.