Related papers: Supersymmetric Picard-Vessiot Theory, I: Basic The…
The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of…
We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to the deformed Leibniz rule…
Five dimensional supersymmetric gauge theory compactified on a circle defines an effective N=2 supersymmetric theory for massless fields in four dimensions. Based on the relativistic Toda chain Hamiltonian proposed by Nekrasov, we derive…
We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the super master formula. We attach some Lie…
According to a quite clever but never acknowledged work of E. Vessiot that won the prize of the Acad\'{e}mie des Sciences in 1904, " Differential Galois Theory " (DGT) has mainly to do with the study of " Principal Homogeneous Spaces "…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…
For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a unique formally real Picard- Vessiot extension up to…
We introduce the notion of H-equivariant Morita-Takeuchi theory for coalgebras with symmetries given by a Hopf algebra H. A cohomology theory is introduced which classifies the possible lifts of coactions on coalgebras to corresponding…
In this paper, using a Hopf-algebraic method, we construct deformed Poincar\'e SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincar\'e algrebra as our fundamental symmetry, we can see the…
Within the context of the extended bi-spinor gauge theory we describe a new off-shell realization of scalar supersymmetry (s-susy) of massless interacting fields with U(1), U(1) x SU(N) and U(1) x SU(N_1) x SU(N_2) gauge groups. S-susy acts…
Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable…
We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the…
Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of…
Originally developed in the context of quantum field theory, the concept of supersymmetry (SUSY) can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical…
A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear…
In this dissertation we discuss various issues concerning application of the Dijkgraaf-Vafa (DV) conjecture to the study of supersymmetric gauge theories. The DV approach is very powerful in that it provides a systematic way of computing…
The objective of this paper is to formulate two distinct supersymmetric (SUSY) extensions of the Gauss-Weingarten and Gauss-Codazzi (GC) equations for conformally parametrized surfaces immersed in a Grassmann superspace, one in terms of a…
We study supersymmetric (SUSY) models derived from the ten-dimensional SUSY Yang- Mills theory compactified on magnetized orbifolds, with nonvanishing Fayet-Iliopoulos (FI) terms induced by magnetic fluxes in extra dimensions. Allowing the…
In this paper we develop a differential Galois theory for algebraic Lie-Vessiot systems in algebraic homogeneous spaces. Lie-Vessiot systems are non autonomous vector fields that are linear combinations with time-dependent coefficients of…
Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we…