Related papers: Structure Theory for Second Order 2D Superintegrab…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string…
We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian…
An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central…
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace both in the case where there are not central charges…
The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
We study the solution of the Schlesinger system for the 4-point $\mathfrak{sl}_N$ isomonodromy problem and conjecture an expression for the isomonodromic $\tau$-function in terms of 2d conformal field theory beyond the known $N=2$…
We construct superstring theories that obey the new supersymmetry algebra {Q_a , Q_b}=\gamma_{ab}^{mn} P_{1m} P_{2n}, in a Green-Schwarz formalism, with kappa supersymmetry also of the new type. The superstring is in a system with a…
We prove that every finitely-generated group of homeomorphisms of the 2-dimensional sphere all of whose elements have a finite order which is a power of 2 and so that there exists a uniform bound for the order of group elements is finite.…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second order integrals of motion but does admit one third and one fourth order integral. We also obtain a classical…
The superintegrability of four Hamiltonians $\tilde{H_r} = \lambda\, H_r$, $r=a,b,c,d$, where $H_r$ are known Hamiltonians and $\lambda$ is a certain function defined on the configuration space and depending of a parameter $\kappa$, is…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
As a continuation of our previous papers arXiv:2109.07639 and arXiv:2202.08196, we study the linearized structure of the manifestly $4D, \mathcal{N} = 2$ supersymmetric theory of the cubic couplings of the higher spin gauge superfields to…
In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its…
A new class of noncommutative $k$-algebras (for $k$ an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first order theory is assigned describing models of a…
N=1, d=4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these…