Quantum critical behavior of semisimple gauge theories

Abstract

We study the perturbative phase diagram of semi-simple fermionic gauge theories resembling the Standard Model. We investigate an SU(N) gauge theory with M Dirac flavors where we gauge first an SU(M) L and then an SU (2) (1) of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalisation group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safety free trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics a lá walking is investigated.

Phase structure of completely asymptotically free SU( Nc ) models with quarks and scalar quarks

“…Fundamental theories are, according to Wilson, the ones featuring in the UV noninteracting (free) [1][2][3][4] or interacting (safe) [5,6] fixed points. If multiple couplings are present, one can have complete asymptotic freedom (CAF) [1,[7][8][9][10][11][12][13][14], or safety (CAS) [6,15,16], or mixed possibilities [12,16,17]. Exact nonperturbative results on the possible asymptotically (un)safe nature of supersymmetric gauge theories were investigated in [18] impacting the very existence of timehonored super grand unified theories [19].…”

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

“…A negative sign, i.e. D grav α > 0, preserves the full fixed-point structure of semi-simple gauge theories as analyzed in [1]. It is vital to note that the sign of the gravity contribution is gauge-independent, cf.…”

“…An SU(2) L subgroup of the global SU(M ) L × SU(M ) R global symmetry is gauged, and features the gauge coupling α 2 . At particular values of (N, M ), the system exhibits a fully IR-attractive interacting fixed point as well as two semi-interacting fixed points with one UV-attractive direction [1]. For the gravity-free beta functions, the corresponding results can be found in App.…”

“…3. Following the terminology in [1], we denote the two fixed points which are UV attractive in one direction by FP1 and FP2, and the fully UV attractive one by FP3.…”

Asymptotically safe grand unification

“…It was, in fact, demonstrated in [36] that these supersymmetric cousins are unsafe, along with a much broader class of supersymmetric theories, further extending the one in [37]. The first study of asymptotically safe chiral gauge theories, some of which resembling GUT-like non-supersymmetric theories, appeared in [38] while semi-simple gauge groups in [39]. Asymptotic safety has been invoked by Weinberg [40] to tame quantum gravity [41][42][43][44][45].…”