Permutation orbifolds

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for fusion rule coefficients are presented, together with the relevant mathematical concepts, such as Λ-matrices and twisted dimensions. The arithmetic restrictions implied by the theory for the allowed modular representations in CFT are discussed. The simplest nonabelian example with twist group S₃ is described to illustrate the general theory.     

Gauge symmetries in heterotic asymmetric orbifolds

We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)$(22,6)$-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for _Z3${\mathbf{Z}}_3$ asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns.     

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2$N=2$ minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.     

A mini-landscape of exact MSSM spectra in heterotic orbifolds

We explore a “fertile patch” of the heterotic landscape based on a Z₆-II${\mathbb{Z}}_6\text{-II}$ orbifold with SO(10) and E₆ local GUT structures. We search for models allowing for the exact MSSM spectrum. Our result is that of order 100 out of a total 3×¹⁰⁴$3\times {10}^4$ inequivalent models satisfy this requirement.     

Free-field representation of permutation branes in Gepner models

We consider a free-field realization of Gepner models based on the free-field realization of N = 2 superconformal minimal models. Using this realization, we analyze the A/B-type boundary conditions starting from the ansatz with the left-moving and right-moving free-field degrees of freedom glued at the boundary by an arbitrary constant matrix. We show that the only boundary conditions consistent with the singular vector structure of unitary minimal model representations are given by permutation matrices, thereby yielding an explicit free-field construction of the permutation branes of Recknagel. The text was submitted by the author in English.     

Asymmetric Gepner models III. B-L lifting

In the same spirit as heterotic weight lifting, B-L lifting is a way of replacing the superfluous and ubiquitous U_(1)B–_L$U{(1)}_{B\text{–}L}$ with something else with the same modular properties, but different conformal weights and ground state dimensions. This method works in principle for all variants of (2,2)$(2,2)$ constructions, such as orbifolds, Calabi–Yau manifolds, free bosons and fermions and Gepner models, since it only modifies the universal SO(10)×E₈$\mathit{SO}(10)\times E_8$ part of the CFT. However, it can only yield chiral spectra if the “internal” sector of the theory provides a simple current of order 5. Here we apply this new method to Gepner models. Including exceptional invariants, 86 of them have the required order 5 simple current, and 69 of these yield chiral spectra. Three family spectra occur abundantly.     

Free-field representations and geometry of some Gepner models

The geometry of the k ^K Gepner model, where k + 2 = 2K, is investigated by a free-field representation known as the “bcβγ” system. Using this representation, we directly show that the internal sector of the model is given by Landau-Ginzburg ℂ ^K /ℤ_2K orbifold. Then we consider the deformation of the orbifold by a marginal antichiral-chiral operator. Analyzing the chiral de Rham complex structure in the holomorphic sector, we show that it coincides with chiral de Rham complex of some toric manifold, where toric data are given by certain fermionic screening currents. This allows relating the Gepner model deformed by the marginal operator to a σ-model on the CY manifold realized as a double cover of ℙ ^{K − 1} with ramification along a certain submanifold.     

Asymmetric Gepner models II. Heterotic weight lifting

A systematic study of “lifted” Gepner models is presented. Lifted Gepner models are obtained from standard Gepner models by replacing one of the N=2$N=2$ building blocks and the E₈$E_8$ factor by a modular isomorphic N=0$N=0$ model on the bosonic side of the heterotic string. The main result is that after this change three family models occur abundantly, in sharp contrast to ordinary Gepner models. In particular, more than 250 new and unrelated moduli spaces of three family models are identified. We discuss the occurrence of fractionally charged particles in these spectra.     

Asymmetric orbifolds and higher level models

I introduce a class of string constructions based on asymmetric orbifolds leading to level two models. In particular, I derive in detail various models with gauge groups E₆ and SO(10), including a four generation E₆ model with two adjoint representations. The occurrence of multiple adjoint representations is a generic feature of the construction. In the course of describing this approach, I will address the problem of twist phases in higher twisted sectors of asymmetric orbifolds.     

Minimal standard heterotic string models

Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z₂×Z₂ orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.     

Supersymmetric sigma models and the heterotic string

We define the (1 + 1)-dimensional supersymmetry algebra of type (p, q) to be that generated by p right-handed Majorana-Weyl supercharges and q left-handed ones. We construct the non-linear sigma models with supersymmetry of type (1,0) and (2,0) and discuss their geometry and their relevance to compactifications of the heterotic superstring. The sigma-model anomalies can be cancelled by a mechanism closely related to that used by Green and Schwarz to cancel gravitational and Yang-Mills anomalies for the superstring.     

Four-dimensional heterotic string models with third-integral twists

The massless string states are constructed for a four-dimensional heterotic string model with the U(5) gauge group in the untwisted sector. The complete observable gauge group, quark and lepton generations, Higgs scalar structure, quark and lepton mass matrix, couplings to colour triplet scalars, and gauge symmetry breaking are studied for this model.     

D0-branes in Gepner models and N = 2 black holes

In this paper D-brane boundary states constructed in Gepner models are used to analyze some aspects of the dynamics of DO-branes in Calabi-Yau compactifications of type II theories to four dimensions. It is shown that the boundary states correspond to BPS objects carrying dyonic charges. By analyzing the couplings to closed string fields a correspondence between the DO-branes and extremal charged black holes in N = 2 supergravity is found.     

Two-loop vacuum amplitude in four-dimensional heterotic string models

The two-loop measure of four-dimensional heterotic strings with N=4, 2 and 1 space-time supersymmetry is explicitly calculated. It is shown that the cosmological constants of these models at two loops are zero.     

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. PACS 11.25.Wx, 12.60.Jv, 04.65.+e     

Model building on asymmetric Z3 orbifolds: Non-supersymmetric models

Four-dimensional string models arising in the asymmetric Z₃ orbifold compactifications of the heterotic string are studied. A mechanism for supersymmetry breaking that gives rise to chiral models in four dimensions is presented, and some typical models are discussed. A formalism for calculating one-loop partition functions in Z₃ models is developed. One partition function is constructed that may correspond to a non-supersymmetric, tachyon-free theory, with a vanishing cosmological constant as a consequence of Atkin-Lehner symmetry. The negative result of a search for the model corresponding to this partition function is reported.     

Investigation of quasi-realistic heterotic string models with reduced Higgs spectrum

Quasi-realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1) that leads to supersymmetry breaking. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. A three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions has been presented (Cleaver et al. in Phys. Rev. D 78, 046009, 2008) and it was argued that all the moduli in that model were fixed. The particular property of that model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric internal dimension boundary conditions with respect to the internal fermions associated with the compactified dimensions. This reduction occurred without the need or presence of flat directions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to models with the same internal space but with modified gauge groups: SO(10) or flipped SU(5) subgroup. We show that all the models studied in this paper do admit stringent flat directions. Currently, the only examples of models that do not admit stringent flat directions are the standard-like models of Cleaver et al. (Phys. Rev. D 78, 046009, 2008). We comment on the relationship between flat directions and reduced Higgs in free fermionic models as well as the possible connection between moduli stabilization and model phenomenology.     

Renormalization group analysis of extended electroweak models from the heterotic string

Extended electroweak models need new parameters (including new renormalization-induced gauge-mixing angles) to fix the gauge currents. We present the renormalization group predictions for these parameters in all heterotic string models with one extra, neutral, gauge boson at low energy. The possible matter contents, consistent with perturbative unification and low-energy physics, are determined for any model.