Asymptotically safe and free chiral theories with and without scalars

Abstract

We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.

Non-Abelian Higgs models: Paving the way for asymptotic freedom

“…While the latter may still be a viable ingredient, our present results illustrate that such a property is not necessary for the construction of asymptotically free trajectories. As far as asymptotic safety is concerned, a wide class of gauged Higgs-Yukawa models has recently been identified that allows for a controlled determination of a non-trivial UV limit in terms of an interacting fixed point [36,[97][98][99][100].…”

“…In essence, this can fix the Higgs-to-gauge-boson mass ratio. So far, a concrete model building has not been satisfactory, as no unequivocally convincing model sufficiently similar to the standard model has been identified, though the search is ongoing, see, e.g., [33][34][35][36].…”

Phase structure of completely asymptotically free SU( Nc ) models with quarks and scalar quarks

“…Fundamental theories are, according to Wilson, the ones featuring in the UV noninteracting (free) [1][2][3][4] or interacting (safe) [5,6] fixed points. If multiple couplings are present, one can have complete asymptotic freedom (CAF) [1,[7][8][9][10][11][12][13][14], or safety (CAS) [6,15,16], or mixed possibilities [12,16,17]. Exact nonperturbative results on the possible asymptotically (un)safe nature of supersymmetric gauge theories were investigated in [18] impacting the very existence of timehonored super grand unified theories [19].…”

“…The choice to study these models stems from the past and recent interest in elementary [1,[7][8][9][10][11][12]14] and composite extensions of the standard model featuring scalar quarks both in models of (super) bosonic technicolor [26][27][28][29] as well as in models of composite Higgs dynamics [30][31][32] embodying explicit realizations [33,34] of the partial composite mechanism for standard model mass generation [35]. The underlying realizations 1 of these composite extensions are dubbed "fundamental partial composite theories" [33].…”

Asymptotically safe grand unification

“…It was, in fact, demonstrated in [36] that these supersymmetric cousins are unsafe, along with a much broader class of supersymmetric theories, further extending the one in [37]. The first study of asymptotically safe chiral gauge theories, some of which resembling GUT-like non-supersymmetric theories, appeared in [38] while semi-simple gauge groups in [39]. Asymptotic safety has been invoked by Weinberg [40] to tame quantum gravity [41][42][43][44][45].…”