Theoretical constraints on scalar parameters in the compact 341 model

Theoretical constraints on the scalar potential of the compact 341 model with three quadruplets scalar fields are discussed. It is shown that in order to ensure the good behavior of the potential and the viability of the model, the criteria, such as copositivity, minimization, perturbative unitarity, perturbativity of the scalar couplings and no ghost scalar bosons (scalar bosons masses positivity), are imposed and bounds on the scalar couplings are obtained. Moreover, the existence of the Landau pole in the model imposes stringent limits.

Asymptotically safe QED

High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the gauge coupling, the electron mass and the Pauli spin-field coupling. Renormalization group trajectories emanating from these fixed points correspond to asymptotically safe theories that are free from the Landau pole problem. We analyze the resulting universality classes defined by the fixed points, determine the corresponding critical exponents, study the resulting phase diagram, and quantify the stability of our results with respect to a systematic expansion scheme. We also compute high-energy complete flows towards the long-range physics. We observe the existence of a renormalization group trajectory that interconnects one of the interacting fixed points with the physical low-energy behavior of QED as measured in experiment. Within pure QED, we estimate the crossover from perturbative QED to the asymptotically safe fixed point regime to occur somewhat above the Planck scale but far below the scale of the Landau pole.

Mean-Field Expansion, Regularization Issue, and Multi-Quark Functions in Nambu–Jona-Lasinio Model

In this paper, the results of the investigation of multi-quark equations in the Nambu–Jona-Lasinio (NJL) model in the mean-field expansion are presented. The multi-quark functions have been considered up to the third order of expansion. One of the purposes of our computations is the study of corrections of higher orders to parameters of the model. The important problem of the application of the NJL model is regularization. We compare the NJL model with 4-dimensional cutoff regularization and the dimensionally analytical regularization. We also discuss so-called “predictive regularization” in the NJL model, and a modification of this regularization, which is free of the Landau pole, is proposed. To calculate the high-order corrections, we use the Legendre transform method in the framework of bilocal-source formalism, which allows one effectively to take into consideration the symmetry constraints. A generalization of the mean-field expansion for other types of multi-quark sources is also discussed.

The Electrostrong Relation

In an attempt to eliminate the Landau Pole from QED by borrowing asymptotic freedom fromQCD, I was successful in uniting the coupling constants of the two, respectively, in the Electrostrong relation. The Strong CP problem is also solved proving that there is no need for fine tuning in QCD. The first step however, was improving the measurement for the running of the strongcoupling constant that can be tested experimentally for the energy scale of the QCD integration parameter Λ, offering such a prediction for the first time.

Towards a holographic quark matter crystal

We construct the gravity dual of d = 4, $$ \mathcal{N}=4 $$ N = 4 , SU(N c) super Yang-Mills theory, coupled to N f flavors of dynamical quarks, at non-zero temperature T and nonzero quark density N q. The supergravity solutions possess a regular horizon if T > 0 and include the backreaction of N c color D3-branes and N f flavor D7-branes with N q units of electric flux on their worldvolume. At zero temperature the solutions interpolate between a Landau pole singularity in the ultraviolet and a Lifshitz geometry in the infrared. At high temperature the thermodynamics is directly sensitive to the Landau pole, whereas at low temperature it is not, as expected from effective field theory. At low temperature and sufficiently high charge density we find thermodynamic and dynamic instabilities towards the spontaneous breaking of translation invariance.