Asymptotic safety guaranteed for strongly coupled gauge theories

Abstract

We demonstrate that interacting ultraviolet fixed points in four dimensions exist at strong coupling, and away from large-N Veneziano limits. This is established exemplarily for semisimple supersymmetric gauge theories with chiral matter and superpotential interactions by using the renormalisation group and exact methods from supersymmetry. We determine the entire superconformal window of ultraviolet fixed points as a function of field multiplicities. Results are in accord with the a-theorem, bounds on conformal charges, Seiberg duality, and unitary. We also find manifolds of Leigh-Strassler models exhibiting lines of infrared fixed points. At weak coupling, findings are confirmed using perturbation theory up to three loop. Benchmark models with low field multiplicities are provided including examples with Standard Model-like gauge sectors. Implications for particle physics, model building, and conformal field theory are indicated.

Fixed points in supersymmetric extensions of the standard model

“…Further, comparing exact results with perturbative ones in regimes where the underlying couplings have become of order unity, it is observed that the latter provides fair estimates in some parameter ranges (i.e. field multiplicities), yet poor estimates in others [39]. We conclude that the size of the perturbative…”

“…It must be clear, however, that this criterion is not rigorous, and that it should ultimately be confirmed with higher loops or nonperturbatively. Some additional insights are offered by a recent nonperturbative study of asymptotically safe UV fixed points in SU (N ) × SU (M) supersymmetric gauge theories with matter [39], but with significantly simpler superpotentials than the MSSM extensions studied here. There, the method of a-maximisation [40] has been used, giving non-perturbative access to fixed points and chiral superfield anomalous dimensions.…”

“…Overall fixed points are mostly perturbative (α * 3 1) in the sense of naïve dimensional analysis (31), though with increasing N Y some of the fixed points become borderline perturbative (α * 3 1) or even strongly coupled (α * 3 ≈ 1) such as in the N q,BSM = 0 strand. The latter require further confirmation using higher loops, or non-perturbative methods [39].…”

“…expansion parameter alone is not sufficient to identify the likely range of perturbative control in more complex theories. Therefore, and for the sake of the present study, we adopt the poor man's criterion (31) with the understanding that extensions to higher loop orders or proper non-perturbative studies [39] are called for as soon as fixed point couplings become of order unity. In addition, consistency of findings is also checked against constraints imposed by unitarity and the a-theorem.…”

The three-loop anomalous dimension and the four-loop $β$-function for ${\cal N}=1$ SQED regularized by higher derivatives

“…We believe that it would be also interesting to generalize the results of this paper to the non-Abelian case. Possibly, they will be also useful for investigating fixed point in supersymmetric theories, see, e.g., [80][81][82] and references therein.…”