Abstract
We study four-dimensional gauge theories coupled to fermions in the fundamental and mesonlike scalars. All requisite beta functions are provided for general gauge group and fermion representation. In the regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up to three loop in the gauge and two loop in the Yukawa and quartic couplings. We find that the conformal window of ultraviolet fixed points is narrowed down by finite-$N$ corrections beyond the Veneziano limit. We also find a new infrared fixed point whose main features, such as scaling exponents, UV-IR connecting trajectories, and phase diagram, are provided. Both fixed points collide upon varying the number of fermion flavors ${N}_{\mathrm{f}}$, and conformality is lost through a saddle-node bifurcation. We further revisit the prospect for ultraviolet fixed points in the large-${N}_{\mathrm{f}}$ limit where matter field fluctuations dominate. Unlike at weak coupling, we do not find clear evidence for new scaling solutions even in the presence of scalar and Yukawa couplings.
Highlights
The seminal discovery of asymptotic freedom has established, for the first time, that local quantum field theories can remain well defined and predictive up to highest energies [1,2]
We further investigate the appearance of a new infrared fixed point, which in perturbation theory becomes visible for the first time at three loop
Following earlier conjectures [36,37,38] and a recent point of critique [39], we revisit the availability of fixed points in the regime of large Nf and finite Nc using perturbation theory
Summary
The seminal discovery of asymptotic freedom has established, for the first time, that local quantum field theories can remain well defined and predictive up to highest energies [1,2]. Conformality is lost upon increasing the number of fermion fields, and whether a new conformal regime might be found at strong coupling To these ends, we provide the general expressions for RG equations up to three loop for simple gauge theories with fermions in general irreducible representations, coupled to mesonlike scalars. We further investigate the appearance of a new infrared fixed point, which in perturbation theory becomes visible for the first time at three loop We show that it is responsible for the loss of conformality at high energies through a fixed-point merger, triggered by increasing the number of fermion species Nf. following earlier conjectures [36,37,38] and a recent point of critique [39], we revisit the availability of fixed points in the regime of large Nf and finite Nc using perturbation theory. The Appendix summarizes general expressions for beta functions up to three loop
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