Asymptotic Safety in Quantum Field Theories
Summary
Asymptotic safety provides a framework for defining quantum field theories that remain well behaved at arbitrarily high energies. In contrast to asymptotic freedom, where interactions vanish in the ultraviolet, asymptotic safety posits the existence of a non-trivial ultraviolet fixed point of the renormalisation group flow. At this fixed point, couplings approach finite, scale-invariant values, ensuring that physical observables do not diverge and that the theory is predictive up to the highest energies. Initially proposed in the context of gravity, the concept has been extended to matter and gauge sectors, leading to candidate ultraviolet completions of the Standard Model and models of quantum gravity. Central to these developments are precise determinations of beta functions, the stability of vacuum states, the role of scalar and Yukawa interactions, and the mapping of conformal windows in gauge-fermion systems. Beyond theoretical interest, asymptotic safety offers pathways to novel phenomena such as radiative symmetry breaking, unification scenarios free from Landau poles, and testable signatures in collider and cosmological observations.
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Asymptotic Safety in Quantum Field Theories publication trend
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Technical terms
Asymptotic safety: A property of a quantum field theory in which couplings approach a finite, interacting fixed point at high energy, avoiding divergences and ensuring predictivity.
Renormalisation group flow: The evolution of coupling constants with energy scale, described by differential equations known as beta functions.
Ultraviolet fixed point: A scale-invariant point of the renormalisation group flow reached at high energy where beta functions vanish.
Beta function: A function that quantifies how a coupling constant changes with the logarithm of the energy scale.
Conformal window: The range of parameters (such as number of flavours or colours) for which a gauge theory admits an interacting, scale-invariant fixed point.
References
- Asymptotic safety guaranteed at four-loop order. Physical Review D (2023).
- Conformal window 2.0: The large Nf safe story. Physical Review D (2018).
- UV conformal window for asymptotic safety. Physical Review D (2018).
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