Related papers: Supersymmetric Picard-Vessiot Theory, I: Basic The…
We linearize nonlinear supersymmetry in the Volkov-Akulov (VA) theory for extended SUSY in two dimensional spacetime ($d = 2$) based on the commutator algebra. Linear SUSY transformations of basic component fields for general vector…
We prove that a differential field K is algebraically closed and Picard-Vessiot closed if and only if the differential Galois cohomology group H^1_\partial(K,G) is trivial for any linear differential algebraic group G over K. We give an…
The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanical harmonic oscillator carry over to the study of more…
The constraints of the superfield method in two-dimensional supergravity are adapted to allow for nonvanishing bosonic torsion. As the analysis of the Bianchi identities reveals, a new vector superfield is encountered besides the well-known…
Supersymmetry (SUSY) of Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum…
We describe a Picard-Vessiot theory for differential fields with non algebraically closed fields of constants. As a technique for constructing and classifying Picard-Vessiot extensions, we develop a Galois descent theory. We utilize this…
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…
This paper starts with the most basic SU(5) Grand Unified Theory, coupled to Supergravity. Then it builds a new theory, incorporating the ideas of Suppressed SUSY. Suppressed SUSY is an alternative to the spontaneous breaking of SUSY. It…
The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we…
This paper extends Hopf-Galois theory to infinite field extensions and provides a natural definition of subextensions. For separable (possibly infinite) Hopf-Galois extensions, it provides a Galois correspondence. This correspondence also…
A conceptual bridge is provided between SUSY and the three-Hilbert-space upgrade of quantum theory a.k.a. ${\cal PT}-$symmetric or quasi-Hermitian. In particular, a natural theoretical link is found between SUSY and the presence of Kato's…
We construct N=1 supersymmetry in 4+2 dimensions compatible with the theoretical framework of 2T physics field theory and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their…
The N=1 supersymmetric gauge SU(5) theory with one antisymmetric tensor, n+3 fundamentals and n+4 antifundamentals has dual magnetic descriptions in the infrared. By introducing extra singlet fields and tree level superpotential terms to…
We investigate for the N = 2 supersymmetry (SUSY) a relation between a vector supermultiplet of the linear SUSY and the Volkov-Akulov model of the nonlinear SUSY. We express component fields of the vector supermultiplet in terms of…
Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some…
A formalism of lattice supersymmetry based on a lattice-deformed superalgebra which was originally introduced in the link approach formulation is presented. We propose that the superalgebra can in fact be identified as a Hopf algebra,…
Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the…
In [arXiv:0808.1677] 3 dimensional field theories are proposed to on-shell represent N=8 SUSY algebra and SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphism. They are theories of 8 scalar and 8 spinor matrix fields with Yukawa,…
Inspired by ideas regarding Hermitian NxN matrix fields obeying a non-associative algebra, 3-dimensional N=8 SUSic field theories are proposed to on-shell represent subalgebras of OSp(8|2) and OSp(8|4) groups of SUSY transformations. They…
Let $F/F_{0}$ be a quadratic extension of non-archimedean locally compact fields of residue characteristic $p\neq 2$. Let $R$ be an algebraically closed field of characteristic different from $p$. For $\pi$ a supercuspidal representation of…