One, two, zero: Scales of strong interactions

Abstract

We discuss our results on QCD with a number of fundamental fermions ranging from zero to sixteen. These theories exhibit a wide array of fascinating phenomena which have been under close scrutiny, especially in recent years, first and foremost is the approach to conformality. To keep this review focused, we have chosen scale generation, or lack thereof as a guiding theme, however the discussion will be set in the general framework of the analysis of the phases and phase transitions of strong interactions at zero and nonzero temperature. I. ADDING MATTER : QCD WITH AN ARBITRARY FLAVOR NUMBERUsual QCD dynamics is characterized by spontaneous symmetry breaking and dynamical mass generation, with the associated scale Λ QCD . However, when the number of flavors exceeds a critical number, an infra-red fixed point (IRFP) appears and prevents the coupling from growing large enough to break chiral symmetry. The theory is then scale invariant -even conformal invariant. In the intermediate region, the coupling 'walks' rather than runs between two typical scales -this is the phenomena of scale separation for which our results provide a preliminary evidence. From a general field theory viewpoint, the analysis of the phase diagram of strong interactions as a function of the number of flavor adds to our knowledge of the theoretical basis of strong interactions and their fundamental mechanisms. From a phenomenological viewpoint, this study deals with a class of models which might play a relevant role in model building beyond the standard model (BSM) [1][2][3][4][5][6], which explain the origin of mass using strong coupling mechanisms realized in QCD with a large number of flavors. All these topics are under active scrutiny both theoretically and experimentally A. ConformalityConformal invariance is anticipated to emerge in the non-Abelian gauge theory with many species (flavors) of fermions [59][60][61][62][63]. This is due to the IRFP for N f > N * f at a coupling which is not strong enough to break chiral symmetry: a second zero of the two-loop beta-function of a non-Abelian gauge theory implies, at least perturbatively, the appearance of IRFP conformal symmetry [59,60]. In color SU(3) gauge theory with N f massless fundamental fermions, the second zero appears at N f 8.05, before the loss of asymptotic freedom (LAF) B. Pre-conformalityThe direct inspection of theories at fixed N f is often inconclusive, especially close to the expected threshold N * f . An alternative approach to establish the existence of the conformal window is to (try to) observe directly the approach to conformality by monitoring the evolution of the results obtained in the broken phase as a function of N f .Moreover, the pre-conformal dynamics at flavor numbers just before the onset of conformal invariance might serve as a paradigm for the BSM model buildings that invokes non-perturbative mechanisms of electroweak symmetry breaking [3][4][5][6]. In such pre-conformal region, the coupling should vary little -should walk -with the scale, at

Massive holographic QCD in the Veneziano limit

“…Knowledge of the dependence of the meson masses on m q near the walking regime is important for the lattice studies which take place at finite quark mass, and aim to locate the conformal transition at m q = 0 [29,75]. As we have pointed out above, the regime B extends even to x < x c (see figure 2), and the crossover between regimes A and B moves to lower x as m q is increased.…”

“…However, it has also been suggested that the transition is discontinuous, such that the dynamics "jumps" and walking is absent [23]. There is an ongoing effort to clarify these issues by using first-principles lattice simulations [24][25][26][27][28][29], but as it turns out, obtaining reliable results in the transition region is difficult.…”

Bifurcations in the RG-Flow of QCD

“…The transition at the lower edge could be first order [26,27] or infinite order [4,22], and can be analyzed through several methods. This is an important open problem as characterization of this phase transition will lead to a better understanding of the strong interactions and might be relevant for model building beyond the standard model [27]. Furthermore, functional RG and holographic approaches indicate that the conformal window is continuously connected to the quark gluon plasma phase at finite temperature [28][29][30].…”

Holography and the conformal window in the Veneziano limit

“…However, it has also been suggested that the transition is discontinuous [3]. There is an ongoing effort to study the theories near the transition by using lattice simulations [4][5][6][7], but as it turns out, obtaining reliable results is much more difficult than for ordinary QCD.…”