Related papers: Composite Supersymmetries in low-dimensional syste…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and…
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it…
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared $SU(N) \leftrightarrow U(k)$ duality involving gauge-singlet fields on one of the two sides. It shares…
We analyse the highest weight representations of the N=1 Ramond algebra and show that their structure is richer than previously suggested in the literature. In particular, we show that certain Verma modules over the N=1 Ramond algebra…
We discuss various questions which emerge in connection with the Lie-algebraic deformation of $\mathbb{CP}^1$ sigma model in two dimensions. First we supersymmetrize the original model endowing it with the minimal ${\cal N}=(0,2)$ and…
Supersymmetry is an algebraic property of a quantum Hamiltonian that, by giving every boson a fermionic superpartner and vice versa, may underpin physics beyond the Standard Model. Fractional bosonic and fermionic quasiparticles are…
We study the spectrum generating closed nonlinear superconformal algebra that describes $\mathcal{N}=2$ super-extensions of rationally deformed quantum harmonic oscillator and conformal mechanics models with coupling constant $g=m(m+1)$,…
In 2+1 dimensions, we propose a renormalizable non-linear sigma model action which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean Electrodynamics. We first start with the simplest model obtained by null reduction of…
We develop a general setting for N=2 rigid supersymmetric field theories with gauged central charge in harmonic superspace. We consider those N=2 multiplets which have a finite number of off-shell components and exist off shell owing to a…
We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these…
We investigate the microphysics of supersymmetric cosmic strings. In particular we focus on the vortices admitted by N=1 supersymmetric abelian Higgs models. We find the vortex solutions and demonstrate that the two simplest supersymmetric…
We construct the non-minimal linear representations of the N=4 Extended Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the…
Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection…
We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…
We consider N=1,2 superconformal mechanics in 0+1 dimensions and show that if the Hamiltonian is invertible the superconformal generators can be used to construct half of the super Virasoro algebra. The full algebra can be derived if the…
Manifest N=2 supersymmetric Toda systems are constructed from the $sl(n,n+1)$ superalgebras by taking into account their complex structure. In the $n\to \infty$ continuum limit an N=2 extension of the $(2+1)$-dimensional heavenly equation…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such…