Heterotic Orbifold Compactifications Research Articles

U(1)′ coupling constant at low energies from heterotic orbifolds

Additional Abelian gauge interactions are generic to string compactifications. In heterotic string models, gauge coupling unification of such forces and other gauge interactions is natural due to their common origin. In this letter we study systematically the 1-loop running of the coupling constants in effective vacua emerging from Z8 heterotic orbifold compactifications that provide the matter spectrum of the MSSM plus some vectorlike exotics, restricting to vacua that yield a non-anomalous U(1)′ symmetry, gauge coupling unification and the observed values of known gauge couplings. We determine the low-energy value of the U(1)′ coupling constant for different scales of supersymmetry breakdown. We find that the U(1)′ coupling constant is quite restricted in string models to lie in the range 0.46–0.7 for low-scale supersymmetry or 0.44–0.6 in other cases. We argue that the phenomenology of these string vacua should be further explored to solve some extant issues, such as the stability of the Higgs vacuum.

Runaway quintessence, out of the swampland

We propose a simple, well-motivated and robust alternative to a metastable de Sitter vacuum in string theory, consistent with current observations of dark energy and naturally satisfying conjectured swampland constraints. Inflation ends in a supersymmetric Minkowski minimum, with a flat direction that is protected by non-renormalisation theorems. At some scale non-perturbative effects kick in, inducing a runaway scalar potential. The tail of this runaway potential cannot sustain a late-time dominating, slow-roll quintessence. However, the potential always contains a dS maximum. If the modulus starts close to the hilltop, it remains frozen there by Hubble friction for much of the cosmological history, at first sourcing a tiny classical vacuum energy and then constituting a rolling quintessence, with observable consequences. So long as the modulus is localised away from the Standard Model in the extra dimensions, there are no observable fifth forces nor is there time-variation of fundamental constants, and the modulus mass is protected from radiative corrections. We revisit concrete string models based on heterotic orbifold compactifications, and show that their de Sitter extrema satisfy the recently refined dS Swampland Conjecture.

Kähler potential of heterotic orbifolds with multiple Kähler moduli

Aiming at improving our knowledge of the low-energy limit of heterotic orbifold compactifications, we determine at lowest order the Kähler potential of matter fields in the case where more than three bulk Kähler moduli appear. Interestingly, bulk matter fields couple to more than one Kähler modulus, a subtle difference with models with only three Kähler moduli that may provide a tool to address the question of moduli stabilization in these models.

Natural inflation and moduli stabilization in heterotic orbifolds

We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio r ≈ 0.05. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedekind η function. We present two setups inspired by the mini-landscape models of the ℤ6 − II orbifold which realize aligned inflation and stabilization of the relevant moduli. One has a supersymmetric vacuum after inflation, while the other includes a gaugino condensate which breaks supersymmetry at a high scale.

R-charge conservation and more in factorizable and non-factorizable orbifolds

Abstract We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the γ-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the “torus lattice selection rule”. Moreover, we identify a new string selection rule, that we call Rule 6 or the “coset vector selection rule”.

Revisiting coupling selection rules in heterotic orbifold models

We study L-point couplings between twisted sector fields in heterotic orbifold compactifications, using conformal field theory. Selection rules provide an easy way to identify which couplings are non-vanishing. Those used in the current literature are gauge invariance, R-charge conservation and the space group selection rule, but they are not the whole story. We revive and refine a fourth selection rule, due to symmetries in the underlying torus lattice, and introduce a fifth one, due to the existence or not of classical worldsheet instanton solutions to mediate the couplings. We consider briefly the phenomenological consequences of the additional rules, in particular for recent orbifold constructions whose field content correspond to that of the MSSM. The structure of the exotic mass matrices is unaltered and many dimension-5 proton-decay operators vanish.

The orbifolder: A tool to study the low-energy effective theory of heterotic orbifolds

The orbifolder is a program developed in C++ that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum configurations. Program summaryProgram title: orbifolderCatalogue identifier: AELR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELR_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 3No. of lines in distributed program, including test data, etc.: 145 572No. of bytes in distributed program, including test data, etc.: 930 517Distribution format: tar.gzProgramming language:C++Computer: Personal computerOperating system: Tested on Linux (Fedora 15, Ubuntu 11, SuSE 11)Word size: 32 bits or 64 bitsClassification: 11.1External routines: Boost (http://www.boost.org/), GSL (http://www.gnu.org/software/gsl/)Nature of problem: Calculating the low-energy spectrum of heterotic orbifold compactifications.Solution method: Quadratic equations on a lattice; representation theory; polynomial algebra.Running time: Less than a second per model.

Kinetic mixing of U(1)s in heterotic orbifolds

We study kinetic mixing between massless U(1) gauge symmetries in the bosonic formulation of heterotic orbifold compactifications. For non-prime Z_N factorisable orbifolds, we find a simple expression of the mixing in terms of the properties of the N=2 subsectors, which helps understand under what conditions mixing can occur. With this tool, we analyse Z_6-II heterotic orbifolds and find non-vanishing mixing even without including Wilson lines. We show that some semi-realistic models of the Mini-Landscape admit supersymmetric vacua with mixing between the hypercharge and an additional U(1), which can be broken at low energies. We finally discuss some phenomenologically appealing possibilities that hidden photons in heterotic orbifolds allow.

Towards matter ination in heterotic string theory

Recently, a class of inflation models in supergravity with gauge non-singlet matter fields as the inflaton has been proposed. It is based on a `tribrid' structure in the superpotential and on a Heisenberg symmetry for solving the eta-problem. We suggest that a generalization of this model class may be suitable for realising inflation in heterotic orbifold compactifications, where the Heisenberg symmetry is a property of the tree-level K"ahler potential of untwisted matter fields. We discuss moduli stabilization in this setup and propose a mechanism to stabilize the modulus associated to the inflaton, which respects the symmetry in the large radius limit. Inflation ends via a waterfall phase transition, as in hybrid inflation. We give conditions which have to be satisfied for realising inflation along these lines in the matter sector of heterotic orbifolds.

Moduli fixing in semirealistic string compactifications

Heterotic orbifold compactifications yield a myriad of models that reproduce many properties of the supersymmetric extension of the standard model and provide potential solutions to persisting problems of high energy physics, such as the origin of the neutrino masses and the strong CP problem. However, the details of the phenomenology in these scenarios rely on the assumption of a stable vacuum, characterized by moduli fields. In this note, we drop this assumption and address the problem of moduli stabilization in realistic orbifold models. We study their qualities and their 4D effective action, and discuss how nonperturbative effects indeed lift all bulk moduli directions. The resulting vacua are typically de Sitter and there are generically some quasi-flat directions which can help to deal with cosmological challenges, such as inflation.

Quark mass hierarchies in heterotic orbifold GUTs

We discuss how to calculate Yukawa couplings in string-derived orbifold GUTs. As an application we investigate the quark mass hierarchies in these models. An interplay of different mechanisms derived from string theory leads to an interesting pattern. We discuss concrete examples in the context of heterotic orbifold compactifications.

On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds

We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT-like and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the properties observed in our concrete models, which tend to be missed when only “generic” features of a model are assumed. We search for interesting vacua and find several de Sitter solutions, but so far, they all turn out to be unstable.

ORBIFOLD COMPACTIFICATIONS WITH CONTINUOUS WILSON LINES

We identify the untwisted moduli of heterotic orbifold compactifications for the case where the gauge twist is realized by a rotation. The Wilson lines are found to have both continuous and discrete parts. For the case of the standard Z3 orbifold we classify all possibilities of breaking the gauge group E(6) ⊗ SU (3) by nine of the eighteen Wilson moduli and by additional discrete Wilson lines.

Duality transformations for blown-up orbifolds

Assuming that the duality symmetry present for heterotic orbifold compactifications extends to the blow-up orbifold, we derive conditions for the Kähler potential for the moduli and for the cubic Yukawa couplings among the matter fields. This is done, perturbatively in the blowing up procedure, on the level of the low energy effective action. The analysis is based on constraints from N = 2 space-time supersymmetry which are due to the relation between heterotic and type II theories compactified on the same internal space.