Related papers: Supertransvectants and symplectic geometry
Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This…
We study the transverse Poisson structure to adjoint orbits in a complex semi-simple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen quasi-homogeneous coordinates the…
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincar\'e symmetry emerges from the $osp(1|2)$ supersymmetry realized in terms of the deformed…
We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $\kappa$-symmetry for worldline supersymmetry. We…
Using realisations of the positive discrete series representations of the Lie algebra su(1,1) in terms of Meixner-Pollaczek polynomials, the action of su(1,1) on Poisson kernels of these polynomials is considered. In the tensor product of…
We construct an analogue of the Livernet--Loday operad for two compatible brackets. The Livernet--Loday operad can be used to define $\star$-products and deformation quantization for Poisson structures. We make use of our operad in the same…
We extend the study of superinstantons presented in 1905.01513 to include orthosymplectic supergroup gauge theories, $B_{n_0|n_1}$, $C_n$, and $D_{n_0|n_1}$. We utilize equivariant localization to obtain the LMNS contour integral formula…
We present an action for chiral $N=(1,0)$ supergravity in $2+2$ dimensions. The fields of the theory are organized into an $OSp(1|4)$ connection supermatrix, and are given by the usual vierbein $V^a$, spin connection $\omega^{ab}$, and…
We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
We give a new presentation of the Yangian for the orthosymplectic Lie superalgebra $\mathfrak{osp}_{1|2m}$. It relies on the Gauss decomposition of the generator matrix in the $R$-matrix presentation. The defining relations between the…
We study affine osp(1|2) fusion, the fusion in osp(1|2) conformal field theory, for example. Higher-point and higher-genus fusion is discussed. The fusion multiplicities are characterized as discretized volumes of certain convex polytopes,…
In this work we extend Onofri and Perelomov's coherent states methods to the recently introduced $OSp(1/2)$ coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely the homogeneous…
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects…
In this paper we realize the supersymmetric classical $W$-algebras $\mathcal{W}(\overline{\mathfrak{gl}}(n+1|n))$ and $\mathcal{W}(\overline{\mathfrak{gl}}(n|n))$ as differential algebras generated by the coefficients of a monic…
Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…
Operator nucleon vertices are constructed in composite superconformal string model. Splitting of baryon Regge trajectories with the same quantum numbers but with opposite parity is provided by inclusion of simple additional components to…
We derive manifestly locally supersymmetric extensions of the Born-Infeld action with $p=2$. The construction is based on a first order bosonic action for $Dp$-branes with a generalized Weyl invariance.