Four-fermion limit of gauge-Yukawa theories

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 × 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.

Ideal walking dynamics via a gauged NJL model

“…We find numerical evidence to 4 For example, according to recent results, calculable in a perturbative regime, gNJLmodels can be seen as a special case of gauge Yukawa models [50]. A gauge Yukawa model, even when manifestly perturbative, under certain conditions can be viewed as a composite theory [50][51][52][53] and reduce to a gNJL model at a high energy scale. Furthermore, when the gauge coupling runs sufficiently slowly, a gNJL model may be renormalizable with a non-trivial coupling.…”

Fundamental partial compositeness

“…If, on the other hand, quartics become negative at some energy scale, the Coleman-Weinberg mechanism can take place. 7 6 If TC-scalars result from composite fermionic dynamics the intermediate description must abide a number of consistent conditions, known as compositeness conditions, that have been properly re-discussed and extended in [32] for a general class of gauge-Yukawa theories. 7 Although this is not the main focus of this work it is worth mentioning that, if a Coleman-Weinberg phenomenon occurs, one can obtain an elementary Goldstone Higgs, as discussed in appendix B.…”

Quantum critical behavior of semisimple gauge theories

“…It is in addition a non-supersymmetric gauge-Yukawa theory that contains spin-0, spin- 1 2 as well as spin-1 particles. Whereas the literature contains investigations of the phase diagram of semi-simple and simple supersymmetric gauge theories [1][2][3], vector-like fermionic gauge theories [4][5][6][7][8][9][10][11][12], chiral gauge theories [13][14][15], Yukawa theories [16][17][18][19][20] and scalar theories [21] only very little has been done concerning the more general class of theories in which the Standard Model falls [22].…”