相关论文: Component Decompositions and Adynkra Libraries for…

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a…

We consider the supermultiplet of linearized beta-deformation of $\mathcal{N}=4$ Super Yang-Mills(SYM). It was previously studied on the gravitational side. We study the supermultiplet of beta-deformations on the field theory side and we…

Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz…

In the study of supersymmetry in one dimension, various works enumerate sets of generators of garden algebras $GR(d,N)$ (and equivalently, valise Adinkras) for special cases $N = d = 4$ and $N = d = 8$, using group-theoretic methods and…

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the…

We construct new families of deformed supersymmetric field theories which break space-time symmetries but preserve half of the original supersymmetry. We do this by writing deformations as couplings to background multiplets. In many cases…

Presented in this paper the nature of the supersymmetrical representation theory behind 4D, N = 1 theories, as described by component fields, is investigated using the tools of Adinkras and Garden Algebras. A survey of familiar matter…

The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe N=1 supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the…

Adinkras are graphs that can describe off-shell supermultiplets in 1 dimension with a Lie superalgebra known as Garden algebra. In this paper, I show that the degrees of freedom of the adinkra can be represented by a subgraph called a…

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of…

We use the four-dimensional N=2 central charge superspace to give a geometrical construction of the Abelian vector-tensor multiplet consisting, under N=1 supersymmetry, of one vector and one linear multiplet. We derive the component field…

We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…

We define two new indecomposable (not fully reducible) ${\cal N}=8$, $d=1$ off-shell multiplets and consider the corresponding models of ${\cal N}=8$ supersymmetric mechanics with spin variables. Each multiplet is described off shell by a…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\leq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each…

Results are given from a search to form adinkra-like equations based on topologies that are not hypercubes. An alternate class of zonohedra topologies are used to construct adinkra-like graphs. In particular, the rhombic dodecahedron and…

In the Dimension Embedded in Unified Symmetry (Adrian Sabin Popescu, D.E.U.S. (Dimension Embedded in Unified Symmetry), p. 221-247, Ed. Cartea Universitara, Bucuresti, ISBN 978-973-731-519-9 (arXiv:0704.2670) (2007)) book we made a…

Using an interplay between superspace and component superconformal tensor calculus techniques, recently, the off-shell construction of the supersymmetric extension of the three independent curvature-squared invariants for minimal (N = 1)…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…