Composite gauge-bosons made of fermions

TL;DR

This paper constructs fermion-only gauge theories that dynamically produce massless gauge bosons, revealing unique features like the absence of a Noether current and extending to non-Abelian symmetries under specific conditions.

Contribution

It introduces a novel class of fermion-based gauge theories that generate gauge bosons without auxiliary fields, expanding understanding of gauge symmetry emergence from matter fields.

Findings

Massless spin-one bound states appear with correct gauge coupling.

Fermion-antifermion pairs must couple to d-wave states to form gauge bosons.

The Noether current does not exist in these theories, avoiding no-go theorems.

Abstract

We construct a class of Abelian and non-Abelian local gauge theories that consist only of matter fields of fermions. The Lagrangian is compact and local without containing an auxiliary vector field nor a subsidiary condition on the matter fields. Because of the special structure, this Lagrangian can be extended to non-Abelian gauge symmetry only in the case of SU(2) doublet matter fields. We carry out explicit dynamical computation in the leading 1/N order to show that massless spin-one bound states appear with the correct gauge coupling. Our diagram calculation exposes the dynamical features that cannot be explored in the formal auxiliary vector-field trick. For instance, it shows that the s-wave fermion-antifermion interaction alone cannot form the bound gauge-bosons; the fermion-antifermion pairs must couple to the d-wave state too. One feature common to our class of Lagrangian is that the Noether current does not exist. Therefore it evades possible conflict with the no-go theorem of Weinberg and Witten on formation of the non-Abelian gauge bosons.