Related papers: Contact structures and supersymmetric mechanics
We explore ``weak'' supersymmetric systems whose algebra involves, besides Poincare generators, extra bosonic generators not commuting with supercharges. This allows one to have inequal number of bosonic and fermionic 1--particle states in…
A non standard super extensions of the Poincare algebra (S-algebra [1,2]), which seems to be relevant for construction of various D=11 models, are studied. We present two examples of actions for point-like dynamical systems, which are…
N-extended massless arbitrary integer and half-integer spin supermultiplets in four dimensional flat space are studied in the framework of light-cone gauge formalism. For such multiplets, by using light-cone momentum superspace, we build…
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two…
In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.
We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the…
We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For…
We use the supergeometric formalism, more precisely, the so-called "big bracket" (for which brackets and anchors are encoded by functions on some graded symplectic manifold) to address the theory of Jacobi algebroids and bialgebroids…
We consider 5-manifolds with a contact form arising from a hypo structure, which we call \emph{hypo-contact}. We provide conditions which imply that there exists such a structure on an oriented hypersurface of a 6-manifold with a half-flat…
In a previous paper (hep-th/9801040), the superconnection formalism was used to fit the Higgs field into a U(n) gauge theory with particular emphasis on the n=2 case, aiming at the reconstruction of certain parts of the Standard Model. The…
On a manifold with an almost contact metric structure $(\varphi,\vec\xi,\eta,g,X,D)$ the notions of the interior and the $N$-prolonged connections are introduced. Using the $N$-prolonged connection, a new almost contact metric structure is…
The presentation of supergravity theories of our previous paper "Super-Poincare' algebras, space-times and supergravities (I)" is re-formulated in the language of Berezin-Leites-Kostant theory of supermanifolds. It is also shown that the…
We consider super Yang-Mills theory on supermanifolds $\mathcal{M}^{(D|m)}$ using integral forms. The latter are used to define a geometric theory of integration and are essential for a consistent action principle. The construction relies…
A construction of supersymmetric field-theoretical models in non-commutative geometry is reviewed. The underlying superstructure of the models is encoded in $osp(2,2)$ superalgebra.
Bethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional N=2 Poincare supersymmetry with the stationary states of some quantum integrable system. The supersymmetric theory can…
Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
In this contribution, I discuss the role of symmetries and algebraic methods in nuclear structure physics. In particular, I review some recent developments in nuclear supersymmetry and indicate possible applications for light nuclei in the…