Related papers: Supersymmetric Jaynes-Cummings model and its exact…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
The Seiberg-Witten curves and differentials for $\N=2$ supersymmetric Yang-Mills theories with one hypermultiplet of mass $m$ in the adjoint representation of the gauge algebra $\G$, are constructed for arbitrary classical or exceptional…
All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…
We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…
It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…
Supersymmetrical intertwining relations of second order in derivatives allow to construct a two-dimensional quantum model with complex potential, for which {\it all} energy levels and bound state wave functions are obtained analytically.…
These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern-Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane…
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
A superpotential algebra is square if its quiver admits an embedding into a two-torus such that the image of its underlying graph is a square grid, possibly with diagonal edges in the unit squares; examples are provided by dimer models in…
The statistics-altering operators present in the limit $q=-1$ of multiparticle SU_q(2)-invariant subspaces parallel the action of such operators which naturally occur in supersymmetric theories. We illustrate this heuristically by…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…
We study the radial part of the Dunkl-Coulomb problem in two dimensions and show that this problem possesses the $su(1,1)$ symmetry. We introduce two different realizations for the $su(1,1)$ Lie algebra and use the theory of irreducible…
We give a supersymmetric generalization of the sine algebra and the quantum algebra $U_{t}(sl(2))$. Making use of the $q$-pseudo-differential operators graded with a fermionic algebra, we obtain a supersymmetric extension of sine algebra.…
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the…
We make a four-algebraic extension of the IIB matrix model. The extension can be made by any Lie 4-algebra. The four-algebraic model has the same supersymmetry as the IIB matrix model, and hence as type IIB superstring theory. The…
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…
Recent work applying higher gauge theory to the superstring has indicated the presence of `higher symmetry'. Infinitesimally, this is realized by a `Lie 2-superalgebra' extending the Poincare superalgebra in precisely the dimensions where…