arXiv subjects

M. A. Zubkov

Publications and source records attributed to M. A. Zubkov.

At least 127 records · Page 7Linked to original sources

arXiv2009

$Z_6$ symmetry of the Standard Model and Technicolor theory

We consider the possibility to continue the $Z_6$ symmetry of the Standard Model to the Technicolor theories. Among the SU(N) Weinberg - Susskind models and the SU(N) Farhi - Susskind models for $N>2$ only the SU(4) Farhi - Susskind model may possess the mentioned symmetry. We also show that the hypercharge assignment of Minimal Walking SU(2) Technicolor model may be chosen in such a way that the additional discrete symmetry is preserved.

hep-ph↗

arXiv2009

Nambu monopoles in lattice Electroweak theory

We considered the lattice electroweak theory at realistic values of $α$ and $θ_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical objects. However, we have found that their density on the lattice increases with increasing ultraviolet cutoff. Thus we conclude, that the conventional lattice electroweak theory is not able to predict the density of Nambu monopoles. This means that the description of Nambu monopole physics based on the lattice Weinberg - Salam model with finite ultraviolet cutoff is incomplete. We expect that the correct description may be obtained only within the lattice theory that involves the description of TeV - scale physics.

hep-lat↗

arXiv2008

Upper bound on the cutoff in lattice Electroweak theory

We investigate numerically lattice Weinberg - Salam model without fermions for realistic values of the fine structure constant and the Weinberg angle. We also analyze the data of the previous numerical investigations of lattice Electroweak theory. We have found that moving along the line of constant physics when the lattice spacing $a$ is decreased, one should leave the physical Higgs phase of the theory at a certain value of $a$. Our estimate of the minimal value of the lattice spacing is $a_c = [430\pm 40 {\rm Gev}]^{-1}$.

hep-ph↗

arXiv2008

Monopoles in lattice Electroweak theory

There exist several types of monopole - like topological defects in Electroweak theory. We investigate properties of these objects using lattice numerical methods. The intimate connection between them and the dynamics of the theory is established. We find that the density of Nambu monopoles cannot be predicted by the choice of the initial parameters of Electroweak theory and should be considered as the new external parameter of the theory. We also investigate the difference between the versions of Electroweak theory with the gauge groups $SU(2)\otimes U(1)$ and $SU(2)\otimes U(1)/Z_2$. We do not detect any difference at $α\sim {1/128}$. However, such a difference appears in the unphysical region of large coupling constant $α> 0.1$.

hep-lat↗

arXiv2008

Lattice study of monopoles in the Electroweak theory

We investigated numerically properties of Nambu monopoles in lattice Electroweak theory at realistic values of $α$ and $θ_W$. Our choice of parameters of lattice Lagrangian corresponds to large values of the Higgs boson mass $M_H > 2 M_W$. We find that the density of Nambu monopoles cannot be predicted by the choice of the initial parameters of Electroweak theory and should be considered as the new external parameter of the theory. We also investigate the difference between the versions of Electroweak theory with the gauge groups $SU(2)\otimes U(1)$ and $SU(2)\otimes U(1)/Z_2$. We do not detect any difference at $α\sim {1/128}$. However, such a difference appears in the strong coupling region and is related to the properties of monopoles constructed of the hypercharge field.

hep-lat↗

arXiv2007

Monopoles, topology of the Standard Model, and unification of interactions at Tev scale

It is shown that unification of strong and Electroweak interactions at Tev scale may lead to appearance of topologically stable monopoles with masses of the order of 40 Tev. Those monopoles may play an important role in the early Universe, at finite temperature. They may even be condensed at high enough temperature. The lattice model for investigation of this phenomenon is presented.

hep-lat↗

arXiv2007

Gauge invariant discretization of Poincare quantum gravity

In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan space with flat pieces of hypercubic form. We consider the model with squared curvature action and calculate the correspondent lattice action. We construct local measure over the dynamical variables of the lattice model.

hep-lat↗

arXiv2007

The observability of an additional discrete symmetry in the Standard Model

Standard Model may be defined with the additional discrete symmetry, i.e. with the gauge group $SU(3)\times SU(2) \times U(1)/{\cal Z}$ (${\cal Z} = Z_6$, $Z_3$ or $Z_2$) instead of the usual $SU(3)\times SU(2) \times U(1)$. It has the same perturbation expansion as the conventional one. However, it may describe nature in a different way at the energies compared to the triviality bound (of about 1 Tev). In this paper we present a possibility to observe this difference assuming that the gauge group of the Standard Model is embedded into the gauge group of an {\it a priory} unknown model, which describes physics at a Tev scale. This difference is related to the monopole content of the theory. We illustrate our results by consideration of the Petite Unification of quarks and leptons.

hep-ph↗

arXiv2006

$Z_6$ symmetry, electroweak transition, and magnetic monopoles at high temperature

We consider the lattice realization of the Standard Model with an additional $Z_6$ symmetry. Numerical simulations were performed on the asymmetric lattice, which corresponds to the finite temperature theory. Our choice of parameters corresponds to large Higgs masses ($M_H > 90$ Gev). The phase diagram was investigated and has been found to be different from that of the usual lattice realization of the Standard Model. It has been found, that the confinement-deconfinement phase transition lines for the SU(2) and SU(3) fields coincide. The transition line between Higgs and symmetric deconfinement parts of the phase diagram and the confinement-deconfinement transition line meet in a triple point. The transition between Higgs and symmetric parts of the phase diagram corresponds to the finite temperature electroweak transition/crossover. We see for the first time evidence that Nambu monopoles are condensed at $T>T_c$ while at $T<T_c$ their condensate vanishes.

hep-lat↗

arXiv2005

Quantization of empty space

We suggest to use "minimal" choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Riemannian space and metric (or vierbein field) is the dynamical variable. We then suggest to use the simplest acceptable action, that is the squared curvature action. The correspondent model is renormalizable, has the correct classical limit without matter and can be explored using Euclidian path integral formalism. In order to get nonperturbative results one has to put this model on the lattice. While doing so serious problems with measure over dynamical variables are encountered, which were not solved until present. We suggest to solve them using the representation of Riemannian space as a limiting case of Riemann - Cartan space, where the Poincare group connection plays the role of dynamical variable. We construct manifestly gauge invariant discretization of Riemann - Cartan space. Lattice realization of Poincare gauge transformation naturally acts on the dynamical variables of the constructed discretization. There exists local measure invariant under this gauge transformation, which could be used as a basic element of lattice path integral methods. The correspondent lattice model appears to be useful for numerical simulations.

hep-lat↗

arXiv2005

Standard Model with the additional $Z_6$ symmetry on the lattice

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently\cite{BVZ2003}. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In \cite{BVZ2004} we have reported our results on the numerical simulation of the Electroweak sector of the model. In this paper we report our results on the numerical simulation of the full ($SU(3)\otimes SU(2) \otimes U(1)$) model. The phase diagram of the model has been investigated using static quark and lepton potentials. Various types of monopoles have been constructed. Their densities appear to be sensitive to the phase transition lines. Differences between the realizations of the Standard Model which do or do not possess the mentioned $Z_6$ symmetry, are discussed.

hep-lat↗

arXiv2005

Measure in the 2D Regge quantum gravity

We propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund - Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with Lund - Regge measure, where this measure is nonlocal and rather complicated, the models based on our approach can be investigated using the numerical simulations in a rather simple way.

hep-lat↗

arXiv2004

An additional symmetry in the Weinberg - Salam model

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper we report our results on the numerical simulation of its Electroweak sector.

hep-lat↗

arXiv2004

2D $R^2$ gravity in weak coupling limit

2D $R^2$ quantum gravity in infinitely large invariant volume is considered. In weak coupling limit the dynamics is reduced to quantum mechanics of a single degree of freedom. The correspondent two - point Green function is calculated explicitly in Gaussian approximation.

gr-qc↗

arXiv2004

10 D Euclidean dynamical triangulations

We investigate numerically 10 - dimensional Euclidean quantum gravity (with discretized Einstein - Hilbert action) in the framework of the dynamical triangulation approach. For the considered values of the gravitational coupling we observed two phases, the behavior of which is found to be similar to that of the crumpled and elongated phases of 3, 4 and 5 dimensional models. Surprisingly, (for the observed lattice sizes) the natural state of the 10 D system (when the Einstein - Hilbert action is turned off) is found to resemble branched polymer while in the low dimensional systems the natural state belongs to the crumpled phase.

hep-lat↗

arXiv2004

Teleparallel gravity on the lattice

We consider quantum gravity model with the squared curvature action. We construct lattice discretization of the model (both on hypercubic and simplicial lattices) starting from its teleparallel equivalent. The resulting lattice models have the actions that are bounded from below while Einstein equations (without matter) appear in their classical limit.

hep-lat↗

arXiv2003

10 D Euclidean quantum gravity on the lattice

10 D Euclidean quantum gravity is investigated numerically using the dynamical triangulation approach. It has been found that the behavior of the model is similar to that of the lower dimensional models. However, it turns out that there are a few features that are not present in the lower dimensional models.

hep-lat↗

arXiv2003

A hidden symmetry in the Standard Model

We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is constructed that possesses this symmetry.

hep-lat↗