Higher Spin Conformal Currents in Minkowski Space

Using unfolded formulation of free equations for massless fields of all spins we obtain explicit form of higher-spin conformal conserved charges bilinear in 4d massless fields of arbitrary spins.Comment: LaTeX, 10 pages. Corrected typo

Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential

We define a complete set of supertraces on the algebra $SH_N(\nu)$, the algebra of observables of the $N$-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of $N=1$ and $N=2$ to arbitrary $N$. It is shown that $SH_N(\nu)$ admits $q(N)$ independent supertraces where $q(N)$ is a number of partitions of $N$ into a sum of odd positive integers, so that $q(N)>1$ for $N\ge 3$. Some consequences of the existence of several independent supertraces of $SH_N (\nu )$ are discussed such as the existence of ideals in associated $W_{\infty}$ - type Lie superalgebras.Comment: 22 pages, LATE

Multi-field approach in mechanics of structural solids

We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several primitive cells and, accordingly, by increasing the number of vector fields describing the response of the body to external factors. Using this approach, we obtain several continuum models and explore their essential properties by comparison with the original structural models. Static and dynamical problems as well as the stability problems for structural solids are considered. We demonstrate that the multi-field approach gives a way to obtain families of models that generalize classical ones and are valid not only for long-, but also for short-wavelength deformations of the structural solid. Some examples of application of the multi-field theory and directions for its further development are also discussed.Comment: 25 pages, 18 figure

Higher-spin current multiplets in operator-product expansions

Various formulas for currents with arbitrary spin are worked out in general space-time dimension, in the free field limit and, at the bare level, in presence of interactions. As the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. The two-point functions and the higher-spin central charges are evaluated at one loop. As an application, the higher-spin hierarchies generated by the stress-tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.Comment: 19 pages. Introductory paragraph, misprint corrected and updated references. CQG in pres

Master Higher-Spin Particle

We propose a "master" higher-spin (HS) particle system. The particle model relevant to the unfolded formulation of HS theory, as well as the HS particle model with a bosonic counterpart of supersymmetry, follow from the master model as its two different gauges. Quantization of the master system gives rise to a new form of the massless HS equations in an extended space involving, besides extra spinorial coordinates, also a complex scalar one. As solutions to these equations we recover the massless HS multiplet with fields of all integer and half-integer helicities, and obtain new multiplets with a non-zero minimal helicity. The HS multiplets are described by complex wave functions which are holomorphic in the scalar coordinate and carry an extra U(1) charge q. The latter fully characterizes the given multiplet by fixing the minimal helicity as q/2. We construct a twistorial formulation of the master system and present the general solution of the associate HS equations through an unconstrained twistor "prepotential".Comment: 21 pages, minor corrections, version to appear in Class. Quantum Gra