Gauge-Yukawa theories: Beta functions at large Nf

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 and extend the results to semisimple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semisimple 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 semisimple 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 first nontrivial order in 1=N f for the 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.

Analytic coupling structure of large Nf (super) QED and QCD

“…At this order the function β (1) (K)/K 2 must develop a singular behavior for the beta-function to develop a zero as N f → ∞. This indeed happens for QED and QCD, as summarized in [5,9,14]. In this paper we investigate this phenomenon further and make a systematic study of the analytic structure of the 't Hooft coupling expansion of the leading large-N f beta-function for QED, QCD, Super QED (SQED) and Super QCD (SQCD).…”

“…The diagrams that contribute to the beta function at the order 1/N f in QED and QCD are displayed, e.g., in [9]. For the contraction of the diagrams one can use the Mathematica package FeynCalc [34], which performs the trace over Lorentz and Dirac indices in d dimensions.…”

“…Asymptotic freedom is lost for theories at finite number of colors and large number of flavors, and therefore such theories can only be fundamental if they develop an interacting fixed point in the ultraviolet. This cannot occur in perturbation theory without Yukawa interactions [1,17], but it may occur non-perturbatively above a critical number of flavors [9]. To see how this might work, let us schematically consider the leading nontrivial order 1/N f beta-function, which up to a normalization reads β(K)…”

Complete asymptotically safe embedding of the standard model

“…By suitable adjustment of the numbers of colours and flavours, a UV fixed point can be achieved that is arbitrarily weakly coupled. Coupled with the "large flavour" fixed points of [24][25][26][27][28][29] operating for the electroweak gauge couplings, one finds an asymptotically safe extension of the Pati-Salam (PS) theory, that has a UV fixed point with gauge group SU (N C ) × SU (2) L × SU (2) R , and a natural breaking down to the SM gauge group in the IR driven partially by radiative symmetry breaking. The main observation of [2] was that the two kinds of fixed points (Veneziano and large N f ) do not interfere with each other.…”

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].…”