Moduli stabilization and light axion by Siegel modular forms

TL;DR

This paper explores how Siegel modular forms can stabilize multiple moduli in string-inspired theories, revealing the existence of a light axion near fixed points, with explicit models in higher symplectic groups.

Contribution

It provides explicit mechanisms for moduli stabilization using Siegel modular forms in $Sp(4, ext{Z})$ and $Sp(6, ext{Z})$ frameworks, highlighting the emergence of light axions.

Findings

Successful stabilization of multiple moduli at CP-conserving fixed points.

Existence of a light axion when moduli are stabilized near fixed points.

Explicit demonstration in $Sp(4, ext{Z})$ and $Sp(6, ext{Z})$ models.

Abstract

We discuss the stabilization of multiple moduli by utilizing Siegel modular forms in the framework of $Sp(2g,\mathbb{Z})$ modular invariant theories. We derive the stationary conditions at CP-conserving fixed points for a generic modular- and CP-invariant scalar potential. The stabilization of multiple moduli is explicitly demonstrated in $Sp(4,\mathbb{Z})$ and $Sp(6,\mathbb{Z})$ modular invariant scalar potentials. Furthermore, it turns out that there exists a light axion when the moduli are stabilized nearby a fixed point.