Note on moduli stabilization, supersymmetry breaking and axiverse

TL;DR

This paper develops a general ${\cal N}=1$ SUGRA framework for moduli stabilization in the presence of heavy moduli and light string theoretic axions, aiming to realize an axiverse while avoiding tachyonic instabilities. It analyzes stabilization near SUSY solutions and shows that a SUSY breaking Minkowski vacuum can stabilize saxions with masses of order $m_{3/2}$ (typically $2 m_{3/2}$) while keeping axions light, provided heavy moduli are sufficiently massive. The work also discusses the roles of approximate $R$-symmetry, the $R$-axion, and SUSY breaking moduli, including how corrections to $W$ and $K$ can generate hierarchical axion masses, and comments on axions from matter-like fields. Collectively, it highlights how a rich axion sector can emerge from concrete stabilization schemes such as KKLT, racetrack, and D-term setups, with potential cosmological and phenomenological implications.

Abstract

We study properties of moduli stabilization in the four dimensional N = 1 supergravity theory with heavy moduli and would-be saxion-axion multiplets including light string-theoretic axions. We give general formulation for the scenario that heavy moduli and saxions are stabilized while axions remain light, assuming that moduli are stabilized near the supersymmetric solution. One can find stable vacuum, i.e. non-tachyonic saxions, in the non-supersymmetric Minkowski vacua. We also discuss the cases, where the moduli are coupled to the supersymmetry breaking sector and/or moduli have contributions to supersymmetry breaking. We also study the models with axions originating from matter-like fields. Our analysis on moduli stabilization is applicable even if there are not light axion multiplets.