Modulus stabilisation in the multiple-modulus framework

TL;DR

This paper explores a mechanism for stabilizing multiple moduli in modular-invariant models, achieving de Sitter vacua at specific fixed points, with implications for lepton flavor mixing.

Contribution

It introduces a stabilisation mechanism for multiple moduli that yields de Sitter minima at fixed points, considering non-perturbative effects and additional Kähler moduli.

Findings

dS vacua can be stabilized at fixed points τ=i and ω

Multiple vacua exist due to additional Kähler moduli

Phenomenological implications for lepton masses and mixing

Abstract

In a class of modular-invariant models with multiple moduli fields, the viable lepton flavour mixing pattern can be realised if the values of moduli are selected to be at the fixed points. In this paper, we investigate a modulus stabilisation mechanism in the multiple-modulus framework which is capable of providing de Sitter (dS) minima precisely at the fixed points $\tau = {\rm i}$ and $\omega$, by taking into consideration non-perturbative effects on the superpotential and the dilaton K\"ahler potential. Due to the existence of additional K\"ahler moduli, more possible vacua can occur, and the dS vacua could be the deepest under certain conditions. We classify different choices of vacua, and discuss their phenomenological implications for lepton masses and flavour mixing.