Moduli stabilization and supersymmetry breaking in heterotic orbifold string models

Abstract

In this paper, we discuss the issues of supersymmetry breaking and moduli stabilization within the context of E 8 E 8 heterotic orbifold constructions and, in particular, we focus on the class of ''minilandscape'' models. In the supersymmetric limit, these models admit an effective low-energy field theory with a spectrum of states and dimensionless gauge and Yukawa couplings very much like that of the minimal supersymmetric standard model. These theories contain a non-Abelian hidden gauge sector which generates a nonperturbative superpotential leading to supersymmetry breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that once supersymmetry is broken in a restricted sector of the theory, then all moduli are stabilized by supergravity effects. Finally, we obtain the low-energy superparticle spectrum resulting from this simple model.

Towards matter ination in heterotic string theory

“…Indeed, a certain class of heterotic orbifolds, the 'mini-landscape' models have been thoroughly studied and shown to yield spectra very close to the MSSM [56][57][58][59][60]. The most recent attempts towards (bulk) moduli stabilization in these models are [61,62], where the latter tries to construct explicit examples. However, there is so far no explicit model with all bulk moduli stabilized.…”

“…Actually, such a violation is necessary since W X should be driven to zero in the waterfall phase transition and we have to stabilize the moduli also afterwards. Recently, a moduli stabilization scheme for heterotic orbifolds was proposed [61], which included the possibility that W = 0 but parametrically small due to the breaking of an approximate R-symmetry at a high order in the superpotential [110]. Here, such a term would induce a slope for the inflaton due to a parametrically small violation of the condition W 0.…”

Searching for the standard model in the string landscape: SUSY GUTs

“…[168]. In general, the model has a perturbative superpotential satisfying modular invariance constraints, an anomalous U(1) A gauge symmetry with a dynamically generated Fayet-Illiopoulos D-term and the hidden QCD-like non-Abelian gauge sector generating a non-perturbative superpotential.…”

“…Thus in Ref. [168] a simple model with a dilaton, S, one volume modulus, T , and three standard model singlets was studied. The model has only one gaugino condensate, as is the case for the "benchmark model 1."…”

Approximate R-symmetries and the μ term

“…We see that the constants Y u , Y d and Z in (3.1) all coincide. We further make the assumption that T and Z are already stabilized (see [25] for a recent discussion; alternative ideas for moduli stabilization are sketched in section 5.2). The structure of the Kähler potential (4.2) is enforced by gauge invariance in higher dimensions.…”