Related papers: Superspace: a Comfortably Vast Algebraic Variety
During the last decades algebraization of space turned out to be a promising tool at the interface between Mathematics and Theoretical Physics. Starting with works by Gel'fand-Kolmogoroff and Gel'fand-Naimark, this branch developed as from…
A large class of supersymmetric extended objects is considered from the viewpoint of embeddings of super worldsurfaces into target superspaces. It is shown that a simple geometrical condition leads to the equations of motion for the brane…
The supersymmetry invariance of flat supergravity (i.e., supergravity in the absence of any internal scale in the Lagrangian) in four dimensions on a manifold with non-trivial boundary is explored. Using a geometric approach we find that…
In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-$BMS_3$, the superconformal algebra and new…
Understanding the emergence of a tangible 4-dimensional space-time from a quantum theory of gravity promises to be a tremendously difficult task. This article makes the case that this task may not have to be carried. Space-time as we know…
The supersymmetric extension of Taub-NUT space admits 4 standard supersymmetries plus several additional non-standard ones. The geometrical origin of these symmetries is traced. The result has applications to fermion modes in gravitational…
Nature's attraction to unique mathematical structures provides powerful hints for unraveling her mysteries. None is at present as intriguing as eleven-dimensional M-theory. The search for exceptional structures specific to eleven dimensions…
An important open question in fundamental physics concerns the nature of spacetime at distance scales associated with the Planck length. The widespread belief that probing such distances necessitates Planck-energy particles has impeded…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
I give an overview of the motivations for and theory/phenomenology of supersymmetry.
We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as $q\to-1$ of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and…
Originally emerged within the context of string and quantum field theory, and later fruitfully extrapolated to photonics, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we…
The usual extensions of supersymmetry require the existence of a complex structure and the formulation of the theory on K\"{a}hler manifolds. It is shown, that by relaxing the constraints on the algebra of supercharges we can get new…
Polygon spaces have been studied extensively, and yet missing from the literature is a simple property that every polygon has: dimension. This is distinct (possibly) from the dimension of the ambient space in which the polygon lives. A…
Super-constrained superfields have provided for most of the best-known and oft-used representations of supersymmetry. The abelian nature of the Lorentz symmetry on the worldsheet turns out to continue permitting the discovery of new…
It has been more than twenty years since theorists started discussing supersymmetric model building/phenomenology. We review mechanisms of supersymmetry breaking/mediation and problems in each scenario. We propose a simple model to address…
There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterize different theories. If it is…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
Following the initial construction of pure supergravity in 1976, various methods were developed to couple supergravity with supersymmetric matter. This contribution to 'Half a century of supergravity' provides a personal perspective on the…