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A. A. Zheltukhin

Publications and source records attributed to A. A. Zheltukhin.

At least 19 recordsLinked to original sources
arXiv2023

On possible composite structure of scalar fields in expanding universe

Scalar fields in curved backgrounds are assumed to be composite objects. As an example realizing such a possibility we consider a model of the massless tensor field $l_{μν}(x)$ in a 4-dim. background $g_{μν}(x)$ with spontaneously broken Weyl and scale symmetries. It is shown that the potential of $l_{μν}$, represented by a scalar quartic polynomial, has the degenerate extremal described by the composite Nambu-Goldstone scalar boson $ϕ(x):=g^{μν}l_{μν}$. Removal of the degeneracy shows that $ϕ$ acquires a non-zero vev $\langleϕ\rangle_{0}=μ$ which, together with the free parameters of the potential, defines the cosmological constant. The latter is zero for a certain choice of the parameters.

hep-th↗
arXiv2020

Brane mechanism of spontaneously generated gravity

The braneworld scenario is studied and the effective action of 3-brane living in 5-dim. Minkowski space is constructed. This action is proved to be invariant under spontaneously broken scale and Weyl symmetries and to encode a model of quadratic gravity generalizing the Starobinsky model. The symmetry breaking generates the Hilbert-Einstein term with the Newton constant $G_{N}\sim\frac{1}{μ^{2}}$, where $μ$ is a mass scale equal to the mean curvature of the vacuum hyper-worldsheet of 3-brane. This result proposes a brane modification of the mechanism of spontaneously generated gravity.

hep-th↗
arXiv2019

$p$-Branes with $AdS_{p+1}$ vacuum as models of $R^2$ gravity

Branes with constant mean curvature of their hyper-worldsheets of codim 1 are treated as the Nambu-Goldstone fields of the broken Poincare symmetry. Mapping of their action into quadratic curvature gravity action with spontaneously generated gravity, is shown. Equation for the brane potential extremals and its solution describing hyper-ws of constant curvature are found. For membranes in $\mathbf{R}^{1,3}$ this extremum is shown to be a saddle 3-dim. hypersurface which defines classically unstable vacuum.

hep-th↗
arXiv2017

Inflation versus collapse in brane matter

Mapping of fundamental branes to their worldsheet (ws) multiplets originating from spontaneous breaking of the Poincare symmetry is studied. The interaction Lagrangian for fields of the Nambu-Goldstone multiplet is shown to encode $R^2$ gravity on the ws. The power law $k_{p}\sim T_{p}^{\frac{3-p}{2(p+1)}}$ for the SO(D-p-1) gauge coupling $k_{p}$ as the function of the p-brane tension $T_{p}$ is assumed. It points to the presence of asymptotic freedom and confinement phases in brane matter. Their connection with collapse and inflation of the branes is discussed.

gr-qc↗
arXiv2017

Phenomenological Lagrangians, gauge models and branes

Phenomenological Lagrangians for physical systems with spontaneously broken symmetries are reformulated in terms of gauge field theory. Description of the Dirac $p$-branes in terms of the Yang-Mills-Cartan gauge multiplets interacting with gravity, is proved to be equivalent to their description as a closed dynamical system with the symmetry $ISO(1,D-1)$ spontaneously broken to $ISO(1,p)\times SO(D-p-1)$.

hep-th↗
arXiv2017

Gauge theory approach to branes and spontaneous symmetry breaking

Gauge theory approach to consideration of the Nambu-Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries, is discussed. The approach is generalized to describe the fundamental branes in terms of $(p+1)$-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu-Goldstone bosons associated with the spontaneously broken Poincare symmetry of the $D$-dimensional Minkowski space.

hep-th↗
arXiv2014

On brane symmetries

The geometric approach to branes is reformulated in terms of gauge vector fields interacting with massless tensor multiplets in gravitational backgrounds

hep-th↗
arXiv2014

Branes as solutions of gauge theories in gravitational field

The idea of the Gauss map is unified with the concept of branes as hypersurfaces embedded into $D$-dimensional Minkowski space. The map introduces new generalized coordinates of branes alternative to their world vectors $\mathbf{x}$ and identified with the gauge and other massless fields. In these coordinates the Dirac $p$-branes realize extremals of the Euler-Lagrange equations of motion of a $(p+1)$-dimensional $SO(D-p-1)$ gauge-invariant action in a gravitational background

hep-th↗
arXiv2012

Laplace-Beltrami operator and exact solutions for branes

Proposed is a new approach to finding exact solutions of nonlinear $p$-brane equations in $D$-dimensional Minkowski space based on the use of various initial value constraints. It is shown that the constraints $Δ^{(p)}\vec{x}=0$ and $Δ^{(p)}\vec{x}=-Λ(t,σ^r)\vec{x}$ give two sets of exact solutions.

hep-th↗
arXiv2012

On nonlinearity of p-brane dynamics

Nonlinear equations of $p$-branes in $D=(2p+1)$-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning $p$-branes with $p=2,3,...,(D-1)/2$ and the Abelian symmetries $U(1)\times U(1)\times... \times U(1)$ of their shapes.

hep-th↗
arXiv2012

Generalized Hooke Law for Relativistic Membranes and p-branes

The character of elastic forces of relativistic membranes and $p$-branes encoded in their nonlinear equations is studied. The toroidal brane equations are reduced to the classical equations of anharmonic elastic media described by monomial potentials. Integrability of the equations is discussed and some of their exact solutions are constructed.

hep-th↗
arXiv2010

Linear space of spinor monomials and realization of the Nambu-Goldstone fermion in the Volkov-Akulov and Komargodski-Seiberg Lagrangians

The analytical algorithm previously proposed by the author for matching the Volkov-Akulov (VA) and Komargodski-Seiberg (KS) actions describing the Nambu-Goldstone (NG) fermion, is discussed. The essence of the algotithm is explained, its consistency is proved and the recent results obtained with computer assistance are reproduced, when the proper Fierz rearrangements for Majorana bispinors are taken into account. We reveal a linear space of composite spinorial monomials $Δ_{m}$ which are the solutions of the scalar constraint $(\partial^{m}\barψΔ_{m})=0$. This space is used to clarify relations between the KS and VA realizations of the NG fermionic field $ψ$.

hep-th↗
arXiv2010

On the cancellation of 4-derivative terms in the Volkov-Akulov action

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fiertz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4-derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac field. Equivalence between the KS and the VA Lagrangians is proved up to the first order in the interaction constant of the NG fermions.

hep-th↗
arXiv2010

U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations

The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the membrane extendedness parameters. The general solution of the Abel equation is constructed. Exact solutions of the whole system of membrane equations in the D=5 Minkowski space-time are found and classified. It is shown that if the radial component of the membrane world vector is only time dependent then the dynamics is described by the pendulum equation.

hep-th↗
arXiv2010

Massless Chiral Supermultiplets of Higher Spins and the $θ$-Twistor

Recently N. Berkovits, motivated by the supertwistor description of ${\cal N}=4 D=4$ super Yang-Mills, considered the generalization of the ${\cal N}=1 D=4$ $θ$-twistor construction to D=10 and applied it for a compact covariant description of ${\cal N}=1 D=10$ super Yang-Mills. This supports the relevance of the $θ$-twistor as a supersymmetric twistor alternative to the well-known supertwistor. The minimal breaking of superconformal symmetry is an inherent property of the $θ$-twistor received from its fermionic components, described by a Grassmannian vector instead of a Grassmannian scalar in the supertwistor. The $θ$-twistor description of the ${\cal N}=1 D=4$ massless chiral supermultiplets $(S, S + 1/2)$ with spins $S=0,1/2,1,3/2,2,...$ is considered here. The description permits to restore the auxiliary $F$ fields of the chiral supermultiplets absent in the supertwistor approach. The proposed formalism is naturally generalized to ${\cal N}=4 D=4 $ and can be used for an off-shell description of the corresponding super Yang-Mills theory.

hep-th↗
arXiv2010

Dmitrij Volkov, super-Poincare group and Grassmann variables

A fundamental role of the Hermann Grassmann anticommuting variables both in physics and mathematics is discussed on the example of supersymmetry. The talk describes how the D. Volkov question about possibility of the existence of Nambu-Goldstone fermions, realized by the Grassmannian variables, resulted in the discovery of the super-Poincare group, its spontaneous breaking and gauging.

hep-th↗