About bosonic rheonomic symmetry and the generation of a spin-1 field in D = 5 supergravity

In this paper we explicitly construct the bosonic sector of supergravity in 5-dimensions using the geometrical approach proposed in a previous publication. Starting from a first-order lagrangian written on an appropriate contraction of the Sp(8) group manifold we find that, in the second-order formalism the particle content of the theory is given by the graviton and by a massless spin-one self-interacting particle. The theory is proved to be factorized and rheonomic symmetrical. The rheonomic symmetry actually guarantees the necessary U(1) gauge invariance of the massless spin-one particle. The lagrangian for the spin-one field is the analogue of the lagrangian of the A_μν? field in D = 11 supergravity.     

Coupling of matter to supergravity from the rheonomic symmetry point of view and the origin of the auxiliary fields

We write a first-order action for the Wess-Zumino supermultiplet regarding it as a 0-form on the graded Poincaré supergroup manifold. The standard supersymmetry transformations are reproduced by the rheonomic symmetry mechanism. When this action is coupled to the geometrical action of supergravity on the group manifold, the same rheonomic symmetry mechanism automatically generates the so-called minimal set of auxiliary fields.     

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so‐called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitatively, and derive for the first time the (temperature—magnetic field) phase diagram, that contains Landau‐Fermi‐liquid, crossover and non‐Fermi liquid parts, thus resembling that of heavy‐fermion compounds.     

Probe‐assisted spin manipulation in one‐dimensional quantum dots

We study a spin structure that arises in a one‐dimensional quantum dot with zero total spin under the action of a charged tip of a scanning probe microscope in the presence of a weak magnetic field. The evolution of spin structure with changing the probe position is traced to show that the movable probe can be an effective tool to manipulate the spin. The spin structures are formed when the probe is located in certain regions along the dot due to Coulomb interaction of electrons as they are redistributed between the two sections in which the quantum dot is divided by the potential barrier created by the probe. There are two main states: spin‐polarized and non‐polarized ones. The transition between them is accompanied by a spin precession governed by the Rashba spin–orbit interaction induced by the electric field of the probe. In the transition region the spin density changes strongly while charge distribution remains nearly unchanged. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

The auxiliary field structure in chirally extended supergravity

The auxiliary fields for Einstein supergravity with axial gauge coupling are those of Maxwell-Einstein supergravity. The gauge algebra is an irreducible extension of the gauge algebra of Einstein supergravity, so that the complete system is a gauge theory with an extra local chiral invariance, rather than a matter coupling.     

Scalar field cosmologies in a Bianchi type I universe

The dynamics of a homogeneous, anisotropic, spatially flat Bianchi type I universe filled with a scalar field is studied. Using the usual synchronous form of the line element, general exact solutions for the Einstein field equations are obtained in the case of the exponential-potential scalar field (V=Λexp(k?)) and in the case of the Barrow-Saich potential ( $V \sim \dot \varphi ^2 $ ). Conditions under which inflation can occur are discussed and the late-time behaviour of the models is also considered.     

Rotating viscous-fluid cosmologies with scalar field and heat flux

Rotating cosmological models under the influence of both shear and bulk viscosity, together with scalar field and heat flow, are studied. Exact solutions of the field equations are obtained. The solutions have nonzero expansion, shear, and rotation. The properties of the solutions are studied and the temperature distribution is also given explicitly.     

Superstrings and the auxiliary field structure of supergravity

We construct the complete superfield of vertex operators corresponding to the four-dimensional N = 1 supergravity multiplet associated with the heterotic superstring. The supergravity fields are shown to consist of a graviton, gravitino, and two auxiliary fields and to form a new minimal supermultiplet. The role of R-invariance in new minimal supergravity is discussed.     

Anisotropic elastic behaviour and one‐dimensional metal in phosphorene

Using first‐principles calculations, we investigate the mechanical and electronic properties of phosphorene nanosheets under tensile strains. It is found that phosphorene possesses a prominent anisotropic elasticity with the large anisotropic factor of 15.5. Along the armchair direction, the phosphorene sheet exhibits a high tensile ductility, characterized by a large elastic strain limit of 0.31. While in the zigzag direction, the critical strain of phosphorene is dictated by the phonon instability and the in‐plane soft mode occurs beyond the 0.22 strain. Under uniaxial strains, the band gaps of phosphorene can be modulated continuously, whose band features are also altered accordingly. A Dirac‐like band structure appears in phosphorene under adequate strains along the zigzag direction. More interestingly, these Dirac cones of phosphorene display evident anisotropy, which have high Fermi velocities up to (6 – 7) × 10⁵ m/s along the armchair direction but drop to zero along the zigzag direction. With such a characteristic, the strained phosphorene sheet acts as an intriguing one‐dimensional metal, which enables the system many potential applications in power‐efficient and ultrafast nanodevices. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

BRS gauge and ghost field supersymmetry in gravity and supergravity

Becchi-Rouet-Stora transformations are obtained for the following systems: (i) Pure Einstein gravity in first order form with vierbein and spin connection as independent fields. (ii) First order Einstein gravity coupled to Yang-Mills fields. (iii) Pure supergravity. For the first two systems the results are as in Yang-Mills theory. But for conventional supergravity the BRS transformations leave the effective action invariant only if the classical equations of motion are satisfied. New transformations of the gauge fields of supergravity have been proposed under which the supersymmetry algebra closes. The corresponding BRS transformations do leave the effective action invariant without the need to use the classical equation of motion; moreover, as in Yang-Mills theories, they are nilpotent and have unit Jacobian.     

2‐branes with Arnold‐Beltrami fluxes from minimal supergravity

We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two‐brane solutions where Arnold‐Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the operator on a three‐torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups Γ.     

Classical integrable systems and gauge field theories

In this review we consider the Hitchin integrable systems and their relations with the self-duality equations and twisted super-symmetric Yang-Mills theory in four dimensions. We define the Symplectic Hecke correspondence between different integrable systems. As an example we consider the Elliptic Calogero-Moser system and integrable Euler-Arnold top on coadjoint orbits of the group GL (N, C) and explain the Symplectic Hecke correspondence for these systems. The text was submitted by the author in English.     

Off‐shell supergravity in five dimensions and supersymmetric brane world scenarios

We review the construction of off‐shell Poincaré supergravity in five dimensions. We describe in detail the minimal multiplet, which is the basic building block, containing the propagating fields of supergravity. All matter multiplets containing (8 + 8) components, being the smallest matter multiplets in five dimensions, are constructed. Using these multiplets the complete tensor calculus for supergravity is developed. As expected it turns out, that there exist three distinct minimal (i.e. containing (48 + 48) field components) off‐shell supergravities. The lagrangians for these theories and their gauged variants are given explicitly. These results are used in the second part to develop a tensor calculus on the orbifold $S^1/\mathbb{Z}_2$. Gauged supergravity on the orbifold $S^1/\mathbb{Z}_2$ with additional cosmological constants at the fixpoints, is constructed. This generalizes the work of Randall‐Sundrum to local supersymmetry. The developed tensor calculus is used to extend this model to include matter located at the fixpoints. Chiral and super Yang‐Mills multiplets at the fixpoints are considered.     

Charge transport in one‐dimensional chains of nanoparticles

Gold electrodes were bridged by a one‐dimensional chain of citrate stabilized gold particles. The resulting device exhibits current fluctuations at constant bias voltage due to conformational changes in the citrate molecules induced by charge transfer across the molecules. Moreover, fluctuations of the differential conductance as a function of the bias voltage became evident. The effect is attributed to the interplay of two origins: (a) dislocation of particles in the chain by action of the electric field; (b) interaction between mechanical motion of citrate molecules located on particles and charge transfer. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The nature of singularities in plane symmetric scalar field cosmologies

The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the Kretschmann scalar diverges uniformly as it is approached. The last fact means in particular that a maximal globally hyperbolic spacetime in this class cannot be extended towards the past through a Cauchy horizon. A subclass of these spacetimes is identified for which the singularity is isotropic.