Modular domain walls and gravitational waves

TL;DR

This paper explores the formation and gravitational wave signatures of modular domain walls in supersymmetric models with modular flavor symmetry, analyzing their evolution, collapse, and potential detectability in current and future experiments.

Contribution

It introduces a novel analysis of modular domain walls in supersymmetric models, including effects of supergravity and their gravitational wave signatures.

Findings

Degenerate vacua at fixed points can produce stable domain walls.

Supergravity effects can lift degeneracy, causing domain wall collapse.

Resulting gravitational waves may be detectable by future experiments.

Abstract

We discuss modular domain walls and gravitational waves in a class of supersymmetric models where quark and lepton flavour symmetry emerges from modular symmetry. In such models a single modulus field $\tau$ is often assumed to be stabilised at or near certain fixed point values such as $\tau = {\rm i}$ and $\tau = \omega$ (the cube root of unity), in its fundamental domain. We show that, in the global supersymmetry limit of certain classes of potentials, the vacua at these fixed points may be degenerate, leading to the formation of modular domain walls in the early Universe. Taking supergravity effects into account, in the background of a fixed dilaton field $S$, the degeneracy may be lifted, leading to a bias term in the potential allowing the domain walls to collapse. We study the resulting gravitational wave spectra arising from the dynamics of such modular domain walls, and assess their observability by current and future experiments, as a window into modular flavour symmetry.