Related papers: Formal Superschemes over Fields: Basic Theory

Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…

If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

A ten-dimensional supersymmetric gauge theory is written in terms of N=1, D=4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken…

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…

Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…

We give an elementary introduction to the structure of supergravity theories. This leads to a table with an overview of supergravity and supersymmetry theories in dimensions 4 to 11. The basic steps in constructing supergravity theories are…

Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact,…

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…

We present scheme theoretic methods that apply to the study of secant varieties. This mainly concerns finite schemes and their smoothability. The theory generalises to the base fields of any characteristic, and even to non-algebraically…

We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum…

These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the…

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex…

The purpose of this paper is to describe and elaborate the philosophical ideas behind hyperstructures and structure formation in general and emphasize the key ideas of the Hyperstructure Program.

A simplicial framework for the gerbe-theoretic modelling of supercharged-loop dynamics in the presence of worldsheet defects is discussed whose equivariantisation with respect to global supersymmetries of the bulk theory and subsequent…

Crossing symmetry provides a powerful tool to access the non-perturbative dynamics of conformal and superconformal field theories. Here we develop the mathematical formalism that allows to construct the crossing equations for arbitrary…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

This Ph.D. thesis investigates effective field and string theories in which supersymmetry is realized and broken in various ways. Chapter 1 addresses effective theories with nonlinearly realized supersymmetry, constructed using the…

This thesis is an exposition of the author's contribution on effective descent morphisms in various categories of generalized categorical structures. It consists of: Chapter 1, where an elementary description of descent theory and the…