The vicinity of the phase transition in the lattice Weinberg - Salam Model

We investigated the lattice Weinberg - Salam model without fermions for the Higgs mass around $300$ GeV. On the phase diagram there exists the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase, where the fluctuations of the scalar field become strong while Nambu monopoles are dense. According to our numerical results (obtained on the lattices of sizes up to $20^3\times 24$) the maximal value of the ultraviolet cutoff in the model cannot exceed the value around $1.4$ TeV.Comment: Proceedings of QUARKS-201

Wigner transformation, momentum space topology, and anomalous transport

Using derivative expansion applied to the Wigner transform of the two - point Green function we analyse the anomalous quantum Hall effect (AQHE), and the chiral magnetic effect (CME). The corresponding currents are proportional to the momentum space topological invariants. We reproduce the conventional expression for the Hall conductivity in $2+1$ D. In $3+1$ D our analysis allows to explain systematically the AQHE in topological insulators and Weyl semimetals. At the same time using this method it may be proved, that the equilibrium CME is absent in the wide class of solids, as well as in the properly regularized relativistic quantum field theory.Comment: Latex, 26 page

How to approach continuum physics in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions numerically for the realistic choice of coupling constants correspondent to the value of the Weinberg angle $\theta_W \sim 30^o$, and bare fine structure constant around $\alpha \sim 1/150$. We consider the values of the scalar self coupling corresponding to Higgs mass $M_H \sim 100, 150, 270$ GeV. It has been found that nonperturbative effects become important while approaching continuum physics within the lattice model. When the ultraviolet cutoff $\Lambda = \frac{\pi}{a}$ (where $a$ is the lattice spacing) is increased and achieves the value around 1 TeV one encounters the fluctuational region (on the phase diagram of the lattice model), where the fluctuations of the scalar field become strong. The classical Nambu monopole can be considered as an embryo of the unphysical symmetric phase within the physical phase. In the fluctuational region quantum Nambu monopoles are dense and, therefore, the use of the perturbation expansion around trivial vacuum in this region is limited. Further increase of the cutoff is accompanied by a transition to the region of the phase diagram, where the scalar field is not condensed (this happens at the value of $\Lambda$ around 1.4 TeV for the considered lattice sizes). Within this region further increase of the cutoff is possible although we do not observe this in details due to the strong fluctuations of the gauge boson correlator. Both mentioned above regions look unphysical. Therefore we come to the conclusion that the maximal value of the cutoff admitted within lattice Electroweak theory cannot exceed the value of the order of 1 TeV.Comment: 19 pages, 15 figures, to appear in Phys.Rev.

Analogies between the Black Hole Interior and the Type II Weyl Semimetals

In the Painleve--Gullstrand (PG) reference frame, the description of elementary particles in the background of a black hole (BH) is similar to the description of non-relativistic matter falling toward the BH center. The velocity of the fall depends on the distance to the center, and it surpasses the speed of light inside the horizon.~Another analogy to non-relativistic physics appears in the description of the massless fermionic particle. Its Hamiltonian inside the BH, when written in the PG reference frame, is identical to the Hamiltonian of the electronic quasiparticles in type~II Weyl semimetals (WSII) that reside in the vicinity of a type~II Weyl point. When these materials are in the equilibrium state, the type II Weyl point becomes the crossing point of the two pieces of the Fermi surface called Fermi pockets. {It was previously stated} that there should be a Fermi surface inside a black hole in equilibrium. In real materials, type II Weyl points come in pairs, and the descriptions of the quasiparticles in their vicinities are, to a certain extent, inverse. Namely, the directions of their velocities are opposite. In line with the mentioned analogy, we propose the hypothesis that inside the equilibrium BH there exist low-energy excitations moving toward the exterior of the BH. These excitations are able to escape from the BH, unlike ordinary matter that falls to its center. The important consequences to the quantum theory of black holes follow.Comment: Latex, 7 page

Torsion instead of Technicolor

We consider the model, which contains a nonminimal coupling of Dirac spinors to torsion. Due to the action for torsion that breaks parity the left - right asymmetry of the spinors appears. This construction is used in order to provide dynamical Electroweak symmetry breaking. Namely, we arrange all Standard Model fermions in the left - handed spinors. The additional technifermions are arranged in right - handed spinors. Due to interaction with torsion technifermions are condensed and, therefore, cause appearance of gauge boson masses. In order to provide all fermions with masses we consider two possibilities. The first one is related to an additional coupling of a real massive scalar field to considered spinors. The second possibility is to introduce the mass term for the mentioned Dirac spinors composed of the Standard Model fermions and the technifermions.Comment: LATEX, to appear in Mod.Phys.Lett.