UV conformal window for asymptotic safety

Abstract

Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete nextto-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.

Aspects of asymptotic safety for quantum gravity

“…In a similar vein, for general 4d quantum field theories without gravity, strict conditions and no-go theorems for asymptotic safety at weak coupling have also been found [102,103]. Interacting fixed points in gauge-matter theories [104][105][106][107][108][109][110] are invariably in accord with the bootstrap. Further examples for exact asymptotic safety include large-N fermionic, scalar, Yukawa, and supersymmetric models in 3d [111][112][113][114][115][116][117][118][119].…”

“…In non-gravitational quantum field theories, Gaussian or near-Gaussian exponents are known to arise either at free or weakly interacting fixed points in large-N limits, e.g. [104][105][106][107][108][109][110] [113][114][115]119]. For interacting fixed points, the appearance of exactly classical exponents is then traced back to the existence of an exactly marginal coupling.…”

Asymptotic safety with Majorana fermions and new large N equivalences

“…Once asymptotic freedom is lost, it develops a weakly interacting asymptotically safe UV fixed point [16] with a stable quantum vacuum [17]. The corresponding UV conformal window has been determined up to the complete next-to-next-to-leading order in perturbation theory which is three loop in the gauge and two loop in the Yukawa and quartic couplings [23].…”

Safe glueballs and baryons

“…This was first studied in Abelian gauge theory in [1] and in the non-Abelian case in [2]. Recently, there has been a revived interest in asymptotically safe four-dimensional quantum field theories, with particular emphasis on pure fermionic gauge theories, chiral gauge theories, gauge-Yukawa theories involving both scalars and fermions and theories with or without supersymmetry [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”