Naturally Light Fermions from Dimensional Reduction

TL;DR

This paper demonstrates how a 3D Gross-Neveu model with domain walls can produce effectively light fermions in 2D, exhibiting asymptotic freedom without fine tuning through a brane-world setup.

Contribution

It introduces a novel mechanism where fermions localized on domain walls in a 3D model mimic 2D light fermions with asymptotic freedom, avoiding fine tuning.

Findings

Exponential divergence of 2D correlation length at large wall separation

Effective 2D coupling derived from 3D parameters matches asymptotic freedom

Criticality achieved without fine tuning in the brane-world setup

Abstract

We consider the 3-d Gross-Neveu model in the broken phase and construct a stable brane world by means of a domain wall and an anti-wall. Fermions of opposite chirality are localized on the walls and coupled through the 3-d bulk. At large wall separation \beta the 2-d correlation length diverges exponentially, hence a 2-d observer cannot distinguish this situation from a 2-d space-time. The 3-d 4-fermion coupling and \beta fix the effective 2-d coupling such that the asymptotic freedom of the 2-d model arises. This mechanism provides criticality without fine tuning.