Four-Fermion Limit of Gauge-Yukawa Theories

TL;DR

This paper explores the conditions under which gauge-Yukawa theories at low energies can be mapped to four-fermion interactions at high energies, suggesting some weakly coupled theories may be fundamentally composite.

Contribution

It identifies a parameter space where perturbative gauge-Yukawa theories can have a strongly coupled, composite high-energy limit, expanding the understanding of possible fundamental structures.

Findings

A region of perturbative parameter space supports a composite high-energy limit.

The hierarchy between ultraviolet and infrared scales can be naturally large and separated.

Standard model Higgs sector could be a manifestation of an underlying composite theory.

Abstract

We elucidate and extend the conditions that map gauge-Yukawa theories at low energies into time-honoured gauged four-fermion interactions at high energies. These compositeness conditions permit to investigate theories of composite dynamics through gauge-Yukawa theories. Here we investigate whether perturbative gauge-Yukawa theories can have a strongly coupled limit at high-energy, that can be mapped into a four-fermion theory. Interestingly, we are able to precisely carve out a region of the perturbative parameter space supporting such a composite limit. This has interesting implications on our current view on models of particle physics. As a template model we use an $SU(N_C)$ gauge theory with $N_F$ Dirac fermions transforming according to the fundamental representation of the gauge group. The fermions further interact with a gauge singlet complex $N_F\times N_F$ Higgs that ceases to be a physical degree of freedom at the ultraviolet composite scale, where it gives away to the four-fermion interactions. We compute the hierarchy between the ultraviolet and infrared composite scales of the theory and show that they are naturally large and well separated. Our results show that some weakly coupled gauge-Yukawa theories can be viewed, in fact, as composite theories. It is therefore tantalising to speculate that the standard model, with its phenomenological perturbative Higgs sector, could hide, in plain sight, a composite theory.