log(M_Pl/m_3/2)

TL;DR

The paper proposes a new mechanism for moduli stabilization and supersymmetry breaking in string theory, replacing a constant superpotential term with a dynamical Chern--Simons term, leading to a hierarchy of scales and a novel mirage mediation scheme.

Contribution

It introduces a dynamical approach to superpotential constants using a continuous Chern--Simons term, resulting in a new supersymmetry breaking mediation scheme called mirage mediation.

Findings

Hierarchical relation between moduli, gravitino, and soft masses.

Emergence of a small parameter <X> ~ 4π^2 log(M_Pl/m_3/2).

Potential implications for phenomenology and cosmology.

Abstract

Flux compactifications of string theory seem to require the presence of a fine-tuned constant in the superpotential. We discuss a scheme where this constant is replaced by a dynamical quantity which we argue to be a `continuous Chern--Simons term'. In such a scheme, the gaugino condensate generates the hierarchically small scale of supersymmetry breakdown rather than adjusting its size to a constant. A crucial ingredient is the appearance of the hierarchically small quantity exp(-<X>) which corresponds to the scale of gaugino condensation. Under rather general circumstances, this leads to a scenario of moduli stabilization, which is endowed with a hierarchy between the mass of the lightest modulus, the gravitino mass and the scale of the soft terms, m_modulus ~ <X> m_3/2 ~ <X>^2 m_soft. The `little hierarchy' <X> is given by the logarithm of the ratio of the Planck scale and the gravitino mass, <X> ~ log(M_Pl/m_3/2) ~ 4pi^2. This exhibits a new mediation scheme of supersymmetry breakdown, called mirage mediation. We highlight the special properties of the scheme, and their consequences for phenomenology and cosmology.