Related papers: Type A N-fold Supersymmetry and Generalized Bender…
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in…
We consider the dimensional reduction of eleven dimensional supergravity to type IIA in ten dimensions, and study the conditions for supersymmetry in terms of p-form spinor bi-linears of the supersymmetry parameter. For a bosonic solution…
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates;…
We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary…
A new bi-parametric $su(1,1)$ algebraization of the Heun class of equations is explored. This yields additional quasi-polynomial solutions of the form $\{z^{\alpha}P_N(z): \ \alpha \in \mathbb{C}, \ N \in \mathbb{N}_0\}$ to the General Heun…
In these lectures we give a geometrical formulation of N-extended supergravities which generalizes N=2 special geometry of N=2 theories. In all these theories duality symmetries are related to the notion of "flat symplectic bundles" and…
We construct a new invariant of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs), under a couple of assumptions on the general properties of such SQFTs motivated by considerations in heterotic string…
We establish general properties of supersymmetric flow equations and of the superpotential of five-dimensional N = 2 gauged supergravity coupled to vector and hypermultiplets. We provide necessary and sufficient conditions for BPS domain…
We study, in a global uniform manner, the quotient of the ring of polynomials in l sets of n variables, by the ideal generated by diagonal quasi-invariant polynomials for general permutation groups W=G(r,n). We show that, for each such…
A class of quantum superintegrable Hamiltonians defined on a two-dimensional hyperboloid is considered together with a set of intertwining operators connecting them. It is shown that such intertwining operators close a su(2,1) Lie algebra…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
We obtain smooth M-theory solutions whose geometry is a warped product of AdS_5 and a compact internal space that can be viewed as an S^4 bundle over S^2. The bundle can be trivial or twisted, depending on the even or odd values of the two…
We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic…
In this paper, we study the Littlewood theory associated with the quantum super immanants and supersymmetric polynomials, including both the super case and the quantum generalization. In the setting of quantum super Schur-Weyl duality…
We classify four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories with a simple gauge group admitting a large $N$ limit that flow to non-trivial superconformal fixed points in the infrared. We focus on the cases where the large $N$…
The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…
Description of adjoint invariants of general Linear Lie superalgebras $\mathfrak{gl}(m|n)$ by Kantor and Trishin is given in terms of supersymmetric polynomials. Later, generators of invariants of the adjoint action of the general linear…
$1+1$-dimensional $SU(N)$ gauge theory coupled to an adjoint Majorana fermion, also known as adjoint QCD$_2$, has the surprising feature that at fermion mass $\sqrt{\frac{g^2 N}{2 \pi}}$ it exhibits supersymmetry. In this paper, we obtain a…
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\{\textsf{A}, \textsf{A}^*\}\in{\cal A}$ subject to $q-$deformed Dolan-Grady relations. Using…
Three-dimensional N-extended superconformal symmetry is studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz…