Dual versions of N=2 supergravity and spontaneous supersymmetry breaking

In this paper, using a model of N=2 supergravity - vector multiplets interaction with the scalar field geometry $SU(1,m)/SU(m)\otimes U(1)$ as an example, we show that even when the geometry is fixed one can have a whole family of the Lagrangians that differ by the vector field duality transformations. As a byproduct, for this geometry we have constructed a model of (m-1) vector multiplets interacting with the hidden sector admitting spontaneous supersymmetry breaking with two arbitrary scales and without a cosmological term.Comment: 10 pages, LaTeX, IHEP preprint 94-9

On Wilson Criterion

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. The naturally chosen correlation functions converge to the correlation functions of the R-gauge electrodynamics on three- and four-dimensional torus as the lattice spacing approaches zero only for the special scaling. This special scaling depends on a choice of a correlation function system. Another scalings give the degenerate continuum limits. The Wilson criterion for the confinement is ambiguous. The asymptotics of the smeared Wilson loop integral for the large loop perimeters is defined by the density of the loop smearing over a torus which is transversal to the loop plane. When the initial torus radius tends to infinity the correlation functions converge to the correlation functions of the R-gauge Euclidean electrodynamics.Comment: latex, 6 page

Infinite spin fields in d = 3 and beyond

In this paper we consider the frame-like formulation for the so called infinite (continuous) spin representations of the Poincare algebra. In the three dimensional case we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge invariant objects and all the necessary extra fields). Moreover we find the supertransformations for the supermultiplet containing one bosonic and one fermionic fields leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed.Comment: 14 pages, 3 figures. Expanded version of the talks given at "Workshop on higher spin gauge fields", 26-28 April 2017, UMONS, Mons, Belgium and "Ginzburg centennial conference on physics", May 29 - June 03 2017, LPI, Moscow, Russi