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Register a new userWhen was Asymptotic Freedom discovered? or The Rehabilitation of Quantum Field Theory
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G. t Hooft
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We glance back at the short period of the great discoveries between 1970 and 1974 that led to the restablishment of Quantum Field Theory and the discovery of the Standard Model of Elementary Particles, in particular Quantum Chromodynamics, and ask ourselves where we stand now.
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An effective field theory model of the massive Yang-Mills theory is considered. Assuming that the renormalized coupling constants of non-renormalizable interactions are suppressed by a large scale parameter it is shown that in analogy to the non-abelian gauge invariant theory the dimensionless coupling constant vanishes logarithmically for large values of the renormalization scale parameter.
We study four-dimensional gauge theories coupled to fermions in the fundamental and meson-like 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 flavours $N_{rm f}$, and conformality is lost through a saddle-node bifurcation. We further revisit the prospect for ultraviolet fixed points in the large $N_{rm f}$ 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.
We renormalize a six dimensional cubic theory to four loops in the MSbar scheme where the scalar is in a bi-adjoint representation. The underlying model was originally derived in a problem relating to gravity being a double copy of Yang-Mills theory. As a field theory in its own right we find that it has a curious property in that while unexpectedly there is no one loop contribution to the $beta$-function the two loop coefficient is negative. It therefore represents an example where asymptotic freedom is determined by the two loop term of the $beta$-function. We also examine a multi-adjoint cubic theory in order to see whether this is a more universal property of these models.
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.
In a recent paper we considered the type 0 string theories, obtained from the ten-dimensional closed NSR string by a GSO projection which excludes space-time fermions, and studied the low-energy dynamics of N coincident D-branes. This led us to conjecture that the four-dimensional SU(N) gauge theory coupled to 6 adjoint massless scalars is dual to a background of type 0 theory carrying N units of R-R 5-form flux and involving a tachyon condensate. The tachyon background leads to a ``soft breaking of conformal invariance, and we derived the corresponding renormalization group equation. Minahan has subsequently found its asymptotic solution for weak coupling and showed that the coupling exhibits logarithmic flow, as expected from the asymptotic freedom of the dual gauge theory. We study this solution in more detail and identify the effect of the 2-loop beta function. We also demonstrate the existence of a fixed point at infinite coupling. Just like the fixed point at zero coupling, it is characterized by the AdS_5times S^5 Einstein frame metric. We argue that there is a RG trajectory extending all the way from the zero coupling fixed point in the UV to the infinite coupling fixed point in the IR.
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