Gauge-Yukawa theories: Beta functions at large $N_f$

Abstract

We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories featuring also semi-simple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semi-simple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the leading $1/N_f$ Yukawa and quartic beta functions. Our work elucidates, consolidates and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.

arXiv comment29 pages, 9 figures, typo fixed

References in corpus (29)

• Conformal collider physics: Energy and charge correlations
• The Exact Superconformal R-Symmetry Maximizes a
• Asymptotic safety guaranteed
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Upper bound on the Abelian gauge coupling from asymptotic safety
• The QCD beta-function at O(1/N_f)
• Vacuum stability of asymptotically safe gauge-Yukawa theories
• Directions for model building from asymptotic safety
• Nonminimal hints for asymptotic safety
• Large N flavor beta-functions: a recap
• Asymptotically Safe Standard Model via Vector-Like Fermions
• Asymptotically Safe Standard Model Extensions?
• Conformal Window 2.0: The Large $N_f$ Safe Story
• Quantum-gravity predictions for the fine-structure constant
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Asymptotically Safe Grand Unification
• Probing Baryogenesis through the Higgs Self-Coupling
• Constraints on ultraviolet-stable fixed points in supersymmetric gauge theories
• Radiative symmetry breaking from interacting UV fixed points
• Asymptotically Safe Dark Matter
• Framework for an asymptotically safe Standard Model via dynamical breaking
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Gauge contribution to the $1/N_F$ expansion of the Yukawa coupling beta function
• $\beta$-functions in large-$N_f$ supersymmetric gauge theories
• Safe SUSY
• Naturalness of asymptotically safe Higgs
• Large-N supersymmetric beta-functions
• Challenging Asymptotic Freedom
• Safe and free instantons

Cited by in corpus (30)

• Model Building from Asymptotic Safety with Higgs and Flavor Portals
• Gravitational Waves from Pati-Salam Dynamics
• Large $N_f$ quantum field theory
• Safe Pati-Salam
• Assessing Perturbativity and Vacuum Stability in High-Scale Leptogenesis
• Asymptotically Safe QED
• Safe Trinification
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• Safety versus triviality on the lattice
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Safe Clockwork
• A complete asymptotically safe embedding of the Standard Model
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• Asymptotically safe dark matter with gauged baryon number
• The abelian gauge-Yukawa $\beta$-functions at large $N_f$
• The $\beta$-function for Yukawa theory at large $N_f$
• Safe Glueballs and Baryons
• A critical look at $\beta$-function singularities at large $N$
• Minimal SU(5) Asymptotic Grand Unification
• Resummation in QFT with Meijer G-functions
• Perturbative Asymptotic Safety and Its Phenomenological Applications
• An asymptotically safe guide to quantum gravity and matter
• Is asymptotically safe inflation eternal?
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• $a$-theorem at large $N_f$
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• Large $N_f$ for multiple representations
• Renormalization Flow of Nonlinear Electrodynamics
• Asymptotic grand unification in SO(10) with one extra dimension
• Conformal Windows beyond Asymptotic Freedom