Moduli stabilization in finite modular symmetric models

TL;DR

This paper explores how combining multiple modular forms in finite modular symmetric models can lead to stable de Sitter vacua with large moduli, expanding the understanding of moduli stabilization.

Contribution

It demonstrates that multiple modular forms can produce non-trivial, CP-preserving vacua away from fixed points, including de Sitter solutions, which was not shown in single-form cases.

Findings

De Sitter vacua realized with multiple modular forms.

Vacua can be located away from fixed points with large moduli.

CP symmetry is preserved in the obtained vacua.

Abstract

We study vacua of moduli potential consisting of multiple contribution of modular forms in a finite modular symmetry. If the potential is given by a single modular form, the Minkowski vacuum is realized at the fixed point of the modular symmetry. We show that the de Sitter vacuum is realized with a multiple modular form case and obtain a non-trivial vacuum which is away from the fixed point, i.e. a large modulus vacuum expectation value, depending on the choice of the weight and representation of the modular forms. We study these vacua numerically and analytically. It is also found that the vacua obtained in this paper preserve CP symmetry.