Hyperbolic extra-dimensions in particle physics and beyond

TL;DR

This paper explores hyperbolic orbifold compactifications in extra-dimensional theories, highlighting their unique properties and potential implications for particle physics, dark matter stability, and cosmology.

Contribution

It provides a detailed analysis of hyperbolic orbifolds for bulk scalar fields and outlines future directions for fermionic and broader studies in extra-dimensional models.

Findings

Hyperbolic orbifolds have a Dirac spectrum with chiral zero modes.

They exhibit a mass gap separating Kaluza-Klein modes.

Residual discrete symmetries may stabilize dark matter.

Abstract

The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and supersymmetry breaking can be done in different ways. Compactifications based on hyperbolic orbifolds gather a large number of properties that are useful for this problem, like a Dirac spectrum chiral zero modes, a mass gap with the Kaluza-Klein modes, discrete residual symmetries for the stability of dark matter, and interesting cosmological constructions. This shall be explored here for bulk scalar fields, with a roadmap provided for fermionic studies and beyond.