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E. K. Loginov

Publications and source records attributed to E. K. Loginov.

At least 19 recordsLinked to original sources
arXiv2021

Solitons and exotic instantons

In this paper, we study the 't Hooft type instantons in eight dimensions, which satisfy the (anti)self-dual equations $F\wedge F=\pm\ast_8F\wedge F$. Using various designs of such instantons, we find new soliton solutions to the low-energy effective theory of the heterotic fivebrane. We investigate conditions under which these instanton configurations can be identified with the $D$-instantons embedded in the $D7$-brane world volume. Finally, we discuss the relationship between eight-dimensional periodic instantons and monopoles.

hep-th↗
arXiv2021

Exotic instantons in eight dimensions

In this paper, we study the (anti-)self-duality equations $\ast F\wedge F=\pm F\wedge F$ in the eight-dimensional Euclidean space. Using properties of the Clifford algebra $Cl_{0,8}(\mathbb{R})$, we find a new solution to these equations.

hep-th↗
arXiv2021

Nonassociative gauge fields

In this paper, we study the consequences of the assumption that the gauge group $SU(2)$ of the standard model is a nonassociative image of $Spin(3)$. Such an approach allows us to take a different look at the Higgs mechanism and obtain the value of the Weinberg angle in very good agreement with the experiment.

hep-th↗
arXiv2021

Octonionic instantons in eight dimensions

In this letter, we study the instanton moduli space of the eight-dimensional solutions of the self-duality equation $F\wedge F= \ast F\wedge F$. Using the known ADHM-construction of such instantons, we compute the dimension of the space of solutions to this construction. We find a general $N$-instanton solution of the 't Hooft type which depends on $8N+1$ free parameters and investigate the cases $N=2$ and $N=3$ in detail.

hep-th↗
arXiv2016

SU(2/1) gauge-Higgs unification

We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group $SU(2)\times U(1)_{Y}$ is embedded in the graded Lie group $SU(2/1)$. Here we follow original works of Ne'eman and Fairlie believing that bosonic fields take their values in the Lie superalgebra and fermionic fields take their values in its representation space. At the same time, our approach differs significantly. The main one is that while for them the gauge symmetry group is $SU(2/1)$, here we consider only symmetries generated by its even subgroup, i.e., symmetries of the standard electroweak model. The reason is that such formalism fixes the quartic Higgs coupling and at the same time removes the sign and statistics problems. The main result is that the presented model predicts values of the Weinberg angle and the Higgs mass correctly up to the two-loop level. Moreover, the model sets the unification scale coinciding with the electroweak scale and automatically describes the fermions correctly with the correct quark and lepton charges.

hep-ph↗
arXiv2014

Yang-Mills like instantons in eight and seven dimensions

We consider a gauge theory in which a nonassociative Moufang loop takes the place of a structure group. We construct Belavin-Polyakov-Schwartz-Tyupkin (BPST) and t'Hooft like instanton solutions of the gauge theory in seven and eight dimensions.

hep-th↗
arXiv2013

Englert-type solutions of d=11 supergravity

A family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one can also obtain non-flat geometries with torsion. This torsion is given locally by the structure constants of a nonassociative geodesic loop in the affinely connected space.

hep-th↗
arXiv2013

Standard Model gauge coupling unification

We study the low energy evolution of coupling constants of the standard model and show that gauge coupling unification can be achieved at the electroweak scale with a suitable normalization. We choose the grand unification group to be the semidirect product of Spin(8) by S_3. In this case the three low energy gauge couplings and the two scalar self-couplings are determined in terms of two independent parameters. In particular, it gives a precise prediction for the mass of the Higgs boson.

hep-ph↗
arXiv2009

Spontaneous compactification and nonassociativity

We consider the Freund-Rubin-Englert mechanism of compactification of N=1 supergravity in 11 dimensions. We systematically investigate both well-known and some new solutions of the classical equations of motion in 11 dimensions. In particular, we show that any threeform potential in 11 dimension is given locally by the structure constants of a geodesic loop in an affinely connected space.

hep-th↗
arXiv2009

On the gauge coupling unification

We consider a quark-lepton symmetry model of unification of the strong and electromagnetic interactions. The model has the gauge group $SU(4)\times U(1)_{Y}$ and the minimal Higgs structure consisting of one complex quartet of scalar particles. The spontaneous breakdown of the gauge group to $SU(3)_{c}\times U(1)_{em}$ due to nonzero vacuum expectation value of the Higgs quartet provides the simplest realization of the Higgs mechanism which generates masses for gauge bosons, and masses to quarks and leptons. Using the embedding of the gauge group to SU(5), we study the evolution of coupling constants and find a connection of the couplings with the gauge couplings of the standard model.

hep-ph↗
arXiv2008

Classification of BPS equations in higher dimensions

We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a general method allowing to obtain the BPS equations in any dimension. In addition, we find all BPS equations in the Minkowski space of dimension $d\leq6$ and apply the obtained results to the supersymmetric Yang-Mills theories. In conclusion, we discuss the possibility of using the classification to construct soliton solutions of the low-energy effective theory of the heterotic string.

hep-th↗
arXiv2008

Remarks on string solitons

We consider generalized self-duality equations for U(2r) Yang-Mills theory on R^8 with quaternionic structure. We employ the extended ADHM method in eight dimensions to construct exact soliton solutions of the low-energy effective theory of the heterotic string.

hep-th↗
arXiv2007

On a class of gauge theories

We give a framework to describe gauge theory in which a nonassociative Moufang loop takes the place of the structure group. The structure of such gauge theory has many formal similarities with that of Yang-Mills theory. We extend the gauge invariance to this theory and construct an on-shell version of N=1 supersymmetric gauge theory.

hep-th↗
arXiv2007

Simple Bol loops

In this paper we investigate the Bol loops and connected with them groups. We prove an analog of the Doro's theorem for Moufang loops and find a criterion for simplicity of Bol loops. One of the main results obtained is the following: if the right multiplication group of a connected finite Bol loop $S$ is a simple group, then $S$ is a Moufang loop.

math.GR↗
arXiv2005

Multi-Instantons in Higher Dimensions and Superstring Solitons

We construct octonionic multi-instantons for the eight and seven dimensional Yang-Mills theory. Extended soliton solutions to the low-energy heterotic field theory equations of motion are constructed from these octonionic multi-instantons. The solitons describe a string in ten-dimensional Minkowski space, and preserve one and two of the sixteen space-time supersymmetries correspondingly.

hep-th↗
arXiv2005

Multi-instantons and superstring solitons

Multi-instanton solutions in the eight and seven dimensional Yang-Mills fields theory is obtained. Extended-soliton solutions to the low-energy heterotic-field-theory equations of motion is constructed from this higher-dimensional multi-instantons.

hep-th↗
arXiv2005

Multi-instantons in seven dimensions

We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t'Hooft construction of instantons in $d=4$, we find $N$-instanton $7d$ solutions which depend on $8N$ effective parameters and are $E_{6}$-invariant.

hep-th↗