How Heavy Can Moduli Be?

TL;DR

This paper investigates the mass limits of moduli in Kaluza-Klein theories, providing numerical evidence that moduli must be relatively light compared to KK gravitons for the effective theory to be consistent.

Contribution

It introduces a numerical bound on moduli masses relative to KK gravitons, revealing a necessary condition for the consistency of 4D effective theories in KK compactifications.

Findings

Light scalar particles must satisfy (m_sc/m_1KK)^2 ≤ 4/3 for consistency.

The results suggest a limit on how rigidly the compact manifold can be stabilized.

Provides numerical evidence for a universal moduli mass bound in KK theories.

Abstract

In Kaluza-Klein (KK) compactification of gravitational theories, moduli fields, which are scalar fields associated to the deformations of the compact manifold, are typically lighter than the KK gravitons. However, a universal limit on their mass does not seem to exist. We provide numerical evidence that a light scalar particle, with mass ratio to the first KK graviton $(m_{\rm sc}/m_{1KK})^2 \leq {4/3}$, is necessary for the consistency of the $4d$ effective theory of KK gravitons. This can be interpreted as a limit on how rigidly the compact manifold can be stabilized.