Dual realizations of dynamical symmetry breaking

TL;DR

This paper demonstrates the equivalence between a 6D scalar field model with localized Higgs potential and a 4D NJL model, showing how higher-dimensional theories can describe dynamical symmetry breaking.

Contribution

It establishes a duality between a 6D scalar model and a 4D NJL model, including a string theory embedding, highlighting higher-dimensional descriptions of symmetry breaking.

Findings

The 6D scalar model is infrared equivalent to the 4D NJL model.

Classical running effects enhance the four-fermion coupling.

Higher-dimensional models can encode dynamical symmetry breaking.

Abstract

We show the infrared equivalence between a recently proposed model containing a six dimensional scalar field with a four-dimensional localized Higgs type potential and the four-dimensional Nambu-Jona-Lasinio (NJL) model. In the dual NJL description, the fermions are localized at the origin of a large two-dimensional compact space. Due to a classical running effect above the compactification scale, the four-fermion coupling of the NJL model increases from the cutoff scale down to the compactification scale, providing the large Fermi coupling needed for the dynamical symmetry breaking. We also present a string theory embedding of our field-theory construction. On more general grounds, our results suggest that 4d models with dynamical symmetry breaking can be given a higher dimensional description in terms of field theories with nontrivial boundary conditions in the internal space.