Related papers: Exceptionality, Supersymmetry and Non-associativit…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry…
These are a set of lectures presented at the CERN-La Plata-Santiago de Compostella School of Physics, La Plata, May 1997. A brief introduction to the non-perturbative structure of string theory is presented. Various non-perturbative…
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products…
We continue to study the problems of discovering new temporal and spatial properties of neutrinos from the point of the possible multi-dimensional extension the D=(3+1)- special theory of relativity. It is neutrino that can connect our…
We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising…
In these two lectures, delivered at the XXXVII Karpacz Winter School, February 2001, I review some applications of superspace in various topics related to string theory and M-theory. The first lecture is mainly devoted to descriptions of…
We discuss some of the signatures associated with extensions of the Standard Model related to the neutrino and electroweak symmetry breaking sectors, with and without supersymmetry. The topics include a basic discussion of the theory of…
An extended summary of the lecture course given at the V School on Geometry and Physics, Bia\l owe\.za 2016, in which an algebraic approach to differentiation and integration that is characteristic for non-commutative geometry is described.
We review the basic ideas and some theoretical models behind the concept of fullerene-like structures made of $\alpha$-particles. The possibility of such a peculiar nuclear shape developing in a double magic superheavy nucleus with $Z$=120…
Many talks at the 16th Lomonosov Conference, dedicated to Bruno Pontecorvo, detail the remarkable progress in neutrino physics over the last two decades. In this paper, I give an opinionated, and therefore likely inaccurate, review of the…
New phenomenological models of Quantum Gravity have suggested that a Lorentz-Invariant discrete spacetime structure may become manifest through a nonstandard coupling of matter fields and spacetime curvature. On the other hand, there is…
I consider models with non-universal gaugino masses at the gauge coupling unification scale, taking into account the Higgs boson discovery. Viable regions of parameter space are mapped and studied in the case of non-universality following…
We review in a pedagogical manner some of the efforts aiming to extend the gauge/gravity correspondence to non-conformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific…
Fermionic zero modes around non-abelian vortices are shown that they constitute two $N=2$, $d=1$ supersymmetric quantum mechanics algebras. These two algebras can be combined under certain circumstances to form a central charge extended…
The different steps that led us to the discovery of {\em no-scale supergravity} are discussed from a very personal point of view. No-scale supergravity has been heralded as the most promising effective theory that describes physics below…
We analyse the relation between anomalies in their manifestly supersymmetric formulation in superspace and their formulation in Wess-Zumino (WZ) gauges. We show that there is a one-to-one correspondence between the solutions of the…
Invited talk at the conference "Fundamental Interactions: From Symmetries to Black Holes" in honor of Francois Englert, 24 - 27 March, Universite Libre de Bruxelles, Belgium
Gravity mediated supersymmetry breakdown originated from a study of gaugino condensation in a hidden sector. We review this mechanism of supergravity breakdown from the original formulation in the early eighties to its natural…
Particle physics models where there are large hidden extra dimensions are currently on the focus of an intense activity. The main reason is that these large extra dimensions may come with a TeV scale for quantum gravity (or string theory)…