Related papers: Formal Superschemes over Fields: Basic Theory
We present an explicit formulation of supersymmetric Yang-Mills theories from $\D=$ 5 to 10 dimensions in the familiar $\N=1,\D=4$ superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in…
Formal orbifolds are defined in higher dimension. Their \'etale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to…
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite…
Relationality is the paradigmatic conceptual core of general-relativistic gauge field theory. It can be made manifest via the Dressing Field Method (DFM) of symmetry reduction, a systematic tool to achieve gauge-invariance by extracting the…
The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We…
Superconformal field theory with $\mathcal{N}=2$ supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over…
Let $\mathcal{P}$ be a proper smooth formal $\mathcal{V}$-scheme, $X$ a closed subscheme of the special fiber of $\mathcal{P}$, $\mathcal{E} \in F\text{-}D ^\mathrm{b}_\mathrm{coh} (\D ^\dag_{\mathcal{P},\mathbb{Q}})$ with support in $X$.…
In this paper we study flat deformations of real subschemes of $\mathbb{P}^n$, hyperbolic with respect to a fixed linear subspace, i.e. admitting a finite surjective and real fibered linear projection. We show that the subset of the…
These lectures provide an introduction to supersymmetry phenomenology. They include an overview of the Minimal Supersymmetric Standard Model. The notion of soft breaking is explained, constraints on the standard soft breaking parameters are…
We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.
We briefly cover the early history of supersymmetry, describe the relation of SUSY quantum field theories to superstring theories and explain why they are considered a likely tool to describe the phenomenology of high energy particle theory…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
The main ideas behind nuclear supersymmetry are presented, starting from the basic concepts of symmetry and the methods of group theory in physics. We propose new, more stringent experimental tests that probe the supersymmetry…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Given a family of world-sheet superconformal field theories related by marginal deformation, we can formulate superstring field theory based on any of these world-sheet theories. Background independence is the statement that these different…