Related papers: Superstability and Symmetry
We construct a class of simple and calculable theories for the supersymmetry breaking soft terms. They are based on quantum modified moduli spaces. These theories do not break supersymmetry in their ground state; instead we postulate that…
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a weakening of the generalized continuum…
We investigate the relationship between the Eklof-Mekler-Shelah Construction Principle for a variety of algebras $\mathbf{V}$ and the question of superstability of the free objects in $\mathbf{V}$, denoted as $\mathcal{F}_\mathbf{V}$. We…
We combine two approaches to the study of classification theory of AECs: 1. that of Shelah: studying non-forking frames without assuming the amalgamation property but assuming the existence of uniqueness triples and 2. that of Grossberg and…
The connection between Supergravity and the low-energy world is analyzed. In particular, the soft Supersymmetry-breaking terms arising in Supergravity, the $\mu$ problem and various solutions proposed to solve it are reviewed. The soft…
A state of matter is characterized by its symmetry breaking and elementary excitations. A supersolid is a state which breaks both translational symmetry and internal $ U(1) $ symmetry. Here, we review some past and recent works in…
A consistent theoretical description of physics at high energies requires an assessment of vacuum stability in either the Standard Model or any extension of it. Especially supersymmetric extensions allow for several vacua and the choice of…
In these Lectures, we present a pedagogical introduction to weak scale supersymmetry phenomenology. A basic understanding of the Standard Model and of the ideas behind Grand Unification, but no prior knowledge of supersymmetry, is assumed.…
In supersymmetric models with the run-away vacua or with the stable but non-supersymmetric ground state there exist stable field configurations (vacua) which restore one half of supersymmetry and are characterized by constant positive…
We propose a solution to the $\mu$-problem due to the non-universal soft supersymmetry breaking in a class of supersymmetric extensions of the SM with an extra U(1) and the NMSSM. Our scenario resembles an earlier one which has been…
We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $\omega$, and, more generally, by weight matrices $\mathfrak{M}$, and investigate continuity of composition…
These lectures provide a phenomenological introduction to supersymmetry, concentrating on the minimal supersymmetric extension of the Standard Model (MSSM). In the first lecture, motivations are provided for thinking that supersymmetry…
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…
Testing the stability of the electroweak vacuum in any extension of the Standard Model Higgs sector is of great importance to verify the consistency of the theory. Multi-scalar extensions as the Minimal Supersymmetric Standard Model…
For an $\aleph_1$-categorical atomic class, we clarify the space of types over the unique model of size $\aleph_1$. Using these results, we prove that if such a class has a model of size $\beth_1^+$ then it is $\omega$-stable.
Supersymmetric Standard Models (SSMs) with Dirac gauginos have the appealing supersoft property that they only cause finite contributions to scalar masses. Considering gauge mediated SUSY breaking with conformal sequestering and assuming…
For any abstract elementary class (AEC) ${\bf K}$ with $\lambda=LS({\bf K})$, the following holds: 1. $K$ has an axiomatization in $L_{(2^\lambda)^+,\lambda^+}$, allowing game quantification. If ${\bf K}$ has arbitrarily large models, the…
We show that $\beth_{(2^{\operatorname{LS}({\bf K})})^+}$ is the lower bound to the Hanf numbers for the length of the order property and for stability in stable abstract elementary classes (AECs). Our examples satisfy the joint embedding…
Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…
Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…