Related papers: Harmonic-Superspace Transform For N=3 SYM-Equation…
Supersymmetric non--linear $\gs$--models in four dimensions with a $D$--term potentials can sometimes have singular kinetic metric terms. As the kinetic terms of scalar fields and their chiral fermionic partners are determine by this…
We present a new set of supersymmetric stationary solutions of pure N=4,d=4 supergravity (and, hence, of low-energy effective string theory) that generalize (and include) the Israel-Wilson-Perj\'es solutions of Einstein-Maxwell theory. All…
We revisit the (untwisted) superfield approach to one-dimensional multi-particle systems with N=4 superconformal invariance. The requirement of a standard (flat) bosonic kinetic energy implies the existence of inertial (super-)coordinates,…
In the present paper we consider anisotropic cosmological vacuum solutions in (4+1) dimensional general quadratic gravity. In particular, we present a solution with 3 equal and 1 different Hubble parameters, and study its stability. We show…
Nonlinear sigma models (NLSM) in d=3 have many interesting and non-trivial features, which were explored poorly in contrast with NLSM in d=2 and d=4. We present a few results from our study of the perturbative and non-perturbative…
We investigate for N = 3 supersymmetry (SUSY) in D = 2 the algebraic relation between the Volkov-Akulov (VA) model of nonlinear (NL) SUSY and a (renormalizable) SO(3) vector supermultiplet of linear (L) SUSY. We derive SUSY and SO(3)…
Functions of hyperbolic type encode representations on real or complex hyperbolic spaces, usually infinite-dimensional. These notes set up the complex case. As applications, we prove the existence of a non-trivial deformation family of…
We consider D-dimensional supersymmetric gauge theories with 8 supercharges (D<6,$~\mathcal{N}=8$) in the framework of harmonic superspaces. The effective Abelian low-energy action for D=5 contains the free and Chern-Simons terms. Effective…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by…
In this paper, we study harmonic analysis on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. After a careful look at Frobenius reciprocity and transitivity of induction, and the…
In three space dimensions, when a physical system possesses spherical symmetry, the dynamical equations automatically lead to the Legendre and the associated Legendre equations, with the respective orthogonal polynomials as their standard…
The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the…
In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field $(A_\mu)$ and the (anti-)ghost fields $((\bar C)C)$ of the…
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of ${\cal N}=4$ SYM in…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
We construct a new SO(3)$\times$SO(3) invariant non-supersymmetric solution of the bosonic field equations of $D=11$ supergravity from the corresponding stationary point of maximal gauged $N=8$ supergravity by making use of the non-linear…
We investigate the equations of motion in the four-dimensional non-anticommutative N=2 supersymmetric U(1) gauge field theory, in the search for BPS configurations. The BPS-like equations, generalizing the abelian (anti)self-duality…