Related papers: Superconformal change of variables for N=1 Neveu-S…
We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular,…
We demonstrate that commutativity of numerous one-dimensional subalgebras in $W_{1+\infty}$ algebra, i.e. the existence of many non-trivial integrable systems described in recent arXiv:2303.05273 follows from the subset of relations in…
We perform a general study of the issue of metastability for supersymmetry-breaking vacua in theories with N=1 and N=2 global supersymmetry. This problem turns out to capture all the important qualitative features of the corresponding…
In these proceedings we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model…
We study deformed supersymmetry in N=2 supersymmetric U(N) gauge theory in non(anti)commutative N=1 superspace. Using the component formalism, we construct deformed N=(1,1/2) supersymmetry explicitly. Based on the deformed supersymmetry, we…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
The general SU(N) form factor formula is constructed. Exact form factors for the field, the energy momentum and the current operators are derived and compared with the 1/N-expansion of the chiral Gross-Neveu model and full agreement is…
We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N=2n supercharges are explicitly constructed and a class of point singularities compatible with…
The pseudo--spectral decomposition of an $N$--particle antisymmetric 1--body positive--semidefinite operator that corresponds to the canonical convex decomposition into the extreme elements of the dual cone of the set of fermion…
This paper is the third of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we introduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtain…
We consider a deformation of N=1 four dimensional Minkowski superspace where odd coordinates $\theta^{\alpha}$ do not anticommute. We define supersymmetric and associative star product and show how the remaining (anti)commutation relations…
We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…
We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability…
In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…
We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to…
We present theories of N=2 hypermultiplets in four spacetime dimensions that are invariant under rigid or local superconformal symmetries. The target spaces of theories with rigid superconformal invariance are (4n)-dimensional {\it special}…
The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial…
We study the superconformally covariant pseudodifferential symbols defined on N=2 super Riemann surfaces. This allows us to construct a primary basis for N=2 super W_KP^(n)-algebras and, by reduction, for N=2 super W_n-algebras.
We show that supersymmetric Abelian models that are obtained from deformations of those with ${\cal N}=2$ supersymmetry also contain metastable vacua for a wide range of parameters. The deformations we consider are combinations of masses…