Light Moduli in Almost No-Scale Models

TL;DR

This paper explores how quantum effects stabilize the size of an extra dimension in five-dimensional supergravity models, predicting a small scalar mass related to the gravitino mass.

Contribution

It demonstrates that quantum corrections fix the size of the extra dimension in no-scale supergravity models with boundary supersymmetry breaking.

Findings

The size of the extra dimension is stabilized at the GUT scale.

A small scalar mass is predicted, proportional to the gravitino mass.

Quantum effects like Casimir energy and FI terms are crucial for stabilization.

Abstract

We discuss the stabilization of the compact dimension for a class of five-dimensional orbifold supergravity models. Supersymmetry is broken by the superpotential on a boundary. Classically, the size $L$ of the fifth dimension is undetermined, with or without supersymmetry breaking, and the effective potential is of no-scale type. The size $L$ is fixed by quantum corrections to the K\"ahler potential, the Casimir energy and Fayet-Iliopoulos (FI) terms localized at the boundaries. For an FI scale of order $M_\mathrm{GUT}$, as in heterotic string compactifications with anomalous $\U1$ symmetries, one obtains $L \sim 1/M_\mathrm{GUT}$. A small mass is predicted for the scalar fluctuation associated with the fifth dimension, $m_{\rho} \lesssim m_{3/2}/(L M)$.